6th Grade Math Flashcards: Understand Solving Equations And Inequalities

What this deck covers

This deck focuses on Understand Solving Equations And Inequalities, giving you a quick way to review the definitions, rules, and examples that matter most for 6th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Which value in the set $\{1,2,3,4\}$ makes the equation $10-x=6$ true?

Answer: $4$. Since $10-4=6$, only $x=4$ satisfies the equation.

Flashcard 2: Which value in the set $\{0, 2, 4\}$ makes $x^2 = 4$ true?

Answer: $2$. Only $2^2 = 4$ is true; $0^2 = 0$ and $4^2 = 16$.

Flashcard 3: Which value in the set $\{2,3,4\}$ makes the equation $\frac{x}{2}=2$ true?

Answer: $4$. Since rac{4}{2}=2, only $x=4$ satisfies the equation.

Flashcard 4: Which values in the set $\{0, 1, 2, 3\}$ make $x + 2 \ge 4$ true?

Answer: $\{2, 3\}$. Test: $2 + 2 = 4 ge 4$ and $3 + 2 = 5 ge 4$ are true.

Flashcard 5: Which value in the set $\{2, 4, 6\}$ makes $x + 1 = 5$ true?

Answer: $4$. Substitute: $4 + 1 = 5$ is true.

Flashcard 6: Identify whether $x=-2$ is a solution of $x+2<0$.

Answer: No, $x=-2$ is not a solution. $-2+2=0$, which is not less than $0$.

Flashcard 7: Which values are you allowed to test when a set is specified?

Answer: Only values from the specified set. You must choose from the given set, not any arbitrary values.

Flashcard 8: Identify whether $x = 5$ is a solution of $2x + 1 = 11$.

Answer: Yes, because $2(5) + 1 = 11$. Substitution confirms the equation is satisfied.

Flashcard 9: Identify whether $x=4$ is a solution of $2x+1=9$.

Answer: Yes, $x=4$ is a solution. $2(4)+1=8+1=9$, which equals the right side.

Flashcard 10: Which values in the set $\{1,2,3,4\}$ make the inequality $2x \ge 6$ true?

Answer: $3$ and $4$. Since $2(3)=6$ and $2(4)=8$, both are $\ge 6$.

Flashcard 11: Identify whether $x = -2$ is a solution of $x + 5 = 3$.

Answer: Yes, because $-2 + 5 = 3$. Substitution confirms the equation is satisfied.

Flashcard 12: Identify whether $x=0$ is a solution of $7x-4=3$.

Answer: No, $x=0$ is not a solution. $7(0)-4=0-4=-4$, which doesn't equal $3$.

Flashcard 13: Which values in $\{0,1,2,3\}$ satisfy $\frac{x}{2} \geq 1$?

Answer: $x=2,3$. $\frac{2}{2}=1$ and $\frac{3}{2}=1.5$ are both $\geq 1$.

Flashcard 14: Which value in $\{2,3,4,5\}$ makes $\frac{x}{5}=\frac{4}{5}$ true?

Answer: $4$. rac{4}{5}=rac{4}{5}, so $x=4$ works.

Flashcard 15: Which value in the set $\{3,4,5\}$ makes the equation $\frac{x}{5}=1$ true?

Answer: $5$. Since rac{5}{5}=1, only $x=5$ satisfies the equation.

Flashcard 16: Which values in $\{0,2,4,6\}$ satisfy $2x\le 8$?

Answer: $\{0,2,4\}$. $2(0)=0$, $2(2)=4$, $2(4)=8$ all satisfy $le 8$.

Flashcard 17: What is substitution when checking a possible solution?

Answer: Replacing the variable with a given value to test truth. We replace the variable with a number to check if the statement is true.

Flashcard 18: Which values in $\{-1,0,1,2\}$ satisfy $x\ge 1$?

Answer: $\{1,2\}$. Values greater than or equal to 1 are 1 and 2.

Flashcard 19: Which values in \{-2,-1,0,1,2\} make $x^2=4$ true?

Answer: $x=-2$ and $x=2$. Both $(-2)^2=4$ and $2^2=4$ are true.

Flashcard 20: Which value in $\{0,2,4,6\}$ makes $3x=12$ true?

Answer: $4$. $3(4)=12$, so $x=4$ satisfies the equation.

Flashcard 21: Which values in the set $\{-1, 0, 1, 2\}$ make $x - 1 < 1$ true?

Answer: $\{-1, 0, 1\}$. Test each: $-1 - 1 = -2 < 1$, $0 - 1 = -1 < 1$, $1 - 1 = 0 < 1$.

Flashcard 22: Which value in the set $\{1,2,3,4\}$ makes the equation $2(x+1)=10$ true?

Answer: $4$. Since $2(4+1)=2(5)=10$, only $x=4$ satisfies.

Flashcard 23: Which values in $\{1,2,3,4,5\}$ satisfy $x+2>6$?

Answer: $\{5\}$. Only $5+2=7>6$, others give $le 6$.

Flashcard 24: Which value in the set $\{2, 3, 4\}$ makes $\frac{x}{3} > 1$ true?

Answer: $4$. Only rac{4}{3} = 1.33... > 1 is true.

Flashcard 25: What is substitution when checking a solution to $x + 7 = 12$?

Answer: Replace $x$ with the given number and evaluate both sides. This process checks if the equation is satisfied.

Flashcard 26: Which value in the set $\{1, 2, 3\}$ makes $5 - x = 2$ true?

Answer: $3$. Substitute: $5 - 3 = 2$ is true.

Flashcard 27: Which value in the set $\{-1,0,1,2\}$ makes the equation $5-x=4$ true?

Answer: $1$. Since $5-1=4$, only $x=1$ satisfies the equation.

Flashcard 28: Which value in the set $\{1,2,3\}$ makes the inequality $x+2>4$ true?

Answer: $3$. Since $3+2=5>4$, only $x=3$ satisfies the inequality.

Flashcard 29: What does it mean for a value to be a solution of an inequality?

Answer: A value that makes the inequality true when substituted. Substitution verifies if the inequality holds true.

Flashcard 30: Which value in the set $\{1,2,3\}$ makes the equation $2x+1=7$ true?

Answer: $3$. Since $2(3)+1=7$, only $x=3$ satisfies the equation.

Flashcard 31: Which value in $\{1,2,3,4\}$ makes $x+5=8$ true?

Answer: $3$. $3+5=8$, so $x=3$ satisfies the equation.

Flashcard 32: Identify whether $x=-3$ is a solution of $x+2<0$.

Answer: Yes, $x=-3$ is a solution. $-3+2=-1$, which is less than $0$.

Flashcard 33: Which value in the set $\{0, 1, 2\}$ makes $3x = 6$ true?

Answer: $2$. Substitute: $3(2) = 6$ is true.

Flashcard 34: Identify whether $x=-1$ is a solution of $3x+2=-1$.

Answer: Yes, $x=-1$ is a solution. $3(-1)+2=-3+2=-1$, which equals the right side.

Flashcard 35: Which value in the set $\{0,1,2,3\}$ makes the equation $x^2=4$ true?

Answer: $2$. Since $2^2=4$, only $x=2$ satisfies the equation.

Flashcard 36: Which values in the set $\{0,1,2,3\}$ make the inequality $x\le 2$ true?

Answer: $0,1,2$. Values $0$, $1$, and $2$ are all less than or equal to $2$.

Flashcard 37: Find the value in $\{1, 4, 7\}$ that makes $3x - 2 = 19$ true.

Answer: $7$. Substitute: $3(7) - 2 = 21 - 2 = 19$ is true.

Flashcard 38: Which values in the set $\{1, 2, 3, 4\}$ make $10 - 2x > 3$ true?

Answer: $\{1, 2, 3\}$. Test: $10 - 2(1) = 8 > 3$, $10 - 2(2) = 6 > 3$, $10 - 2(3) = 4 > 3$.

Flashcard 39: Which value in the set $\{0,1,2,3\}$ makes the equation $4(x-1)=8$ true?

Answer: $3$. Since $4(3-1)=4(2)=8$, only $x=3$ satisfies.

Flashcard 40: Which value in the set {0,1,2} makes the equation $3x=6$ true?

Answer: $2$. Since $3(2)=6$, only $x=2$ satisfies the equation.

Flashcard 41: What is substitution when checking a possible solution for $x$?

Answer: Replace $x$ with the given value and evaluate both sides. Substitution means plugging in a value for the variable.

Flashcard 42: Which statement correctly describes checking $x=2$ in $x+1=4$?

Answer: Substitute: $2+1=3$, so $x=2$ is not a solution. Shows substitution yields $3 eq 4$, proving it's not a solution.

Flashcard 43: Which values are considered when the problem gives a specified set $S$?

Answer: Only values in $S$ can be solutions. Solutions must come from the given set.

Flashcard 44: Which values in the set $\{0,1,2,3\}$ make the inequality $3-x\ge 2$ true?

Answer: $0$ and $1$. Since $3-0=3ge 2$ and $3-1=2ge 2$, both satisfy.

Flashcard 45: Which values in \{1,2,3,4\} satisfy $x+3\leq 6$?

Answer: $x=1,2,3$. $1+3=4$, $2+3=5$, $3+3=6$ are all $\leq 6$; $4+3=7$ is not.

Flashcard 46: Identify whether $x=5$ is a solution of $2x+1=9$.

Answer: No, $x=5$ is not a solution. $2(5)+1=10+1=11$, which doesn't equal $9$.

Flashcard 47: What does it mean for a value to be a solution of an equation?

Answer: A value that makes the equation true when substituted. Substitution verifies if the equation holds true.

Flashcard 48: What is the first step to check whether $x=4$ is a solution of $2x+1=9$?

Answer: Substitute $4$ for $x$ in $2x+1$ and compare to $9$. Substitution checks if the value satisfies the equation.

Flashcard 49: Which values in $\{0,1,2,3,4\}$ satisfy $x<3$?

Answer: $\{0,1,2\}$. Values less than 3 are 0, 1, and 2.

Flashcard 50: Which values in \{-1,0,1,2\} satisfy $2x-1>1$?

Answer: $x=2$ only. Only $2(2)-1=3$ is greater than $1$.

Flashcard 51: Which values in $\{-3,-2,-1,0,1\}$ satisfy $x-1\le -2$?

Answer: $\{-3,-2,-1\}$. $-3-1=-4$, $-2-1=-3$, $-1-1=-2$ all $le -2$.

Flashcard 52: Which value in $\{1,2,3,4\}$ makes $3(x-1)=6$ true?

Answer: $3$. $3(3-1)=3(2)=6$, so $x=3$ works.

Flashcard 53: Which values in the set $\{-2, -1, 0, 1, 2\}$ make $x^2 \le 1$ true?

Answer: $\{-1, 0, 1\}$. Test: $(-1)^2 = 1$, $0^2 = 0$, $1^2 = 1$ all $le 1$.

Flashcard 54: Which value in $\{1,2,3\}$ makes $2x+3=2x+4$ true?

Answer: None. $2x+3=2x+4$ simplifies to $3=4$, which is false.

Flashcard 55: Which value in $\{2,3,4\}$ makes $2x-1=7$ true?

Answer: $4$. $2(4)-1=8-1=7$, so $x=4$ works.

Flashcard 56: Which value in $\{2,4,6\}$ makes $\frac{x}{3}=2$ true?

Answer: $x=6$. $\frac{6}{3}=2$, which equals the right side.

Flashcard 57: Which values in \{0,1,2,3\} make $x^2=4$ true?

Answer: $x=2$ only. Only $2^2=4$; the other values squared don't equal $4$.

Flashcard 58: What is the first step to check whether $x=4$ satisfies $2x+1=9$?

Answer: Substitute $4$ for $x$ in $2x+1=9$. Replace $x$ with $4$ to evaluate the left side of the equation.

Flashcard 59: What does it mean for a value to be a solution of the equation $x+3=10$?

Answer: It makes the equation true when substituted for $x$. A solution satisfies the equation when plugged in for the variable.

Flashcard 60: Which value in $\{1,2,3,4\}$ makes $5=2x+1$ true?

Answer: $2$. $2(2)+1=5$, so $x=2$ satisfies the equation.

Flashcard 61: Which value in \{1,2,3\} makes $5-x=2$ true?

Answer: $x=3$. $5-3=2$, which equals the right side.

Flashcard 62: Which values in the set $\{1, 2, 3, 4\}$ make $2x \le 6$ true?

Answer: $\{1, 2, 3\}$. Test each: $2(1) = 2 le 6$, $2(2) = 4 le 6$, $2(3) = 6 le 6$.

Flashcard 63: Which value in the set $\{1, 2, 3\}$ makes $\frac{x}{2} = 1$ true?

Answer: $2$. Substitute: rac{2}{2} = 1 is true.

Flashcard 64: Which value in $\{0,1,2,3\}$ makes $4+2x=10$ true?

Answer: $3$. $4+2(3)=4+6=10$, so $x=3$ satisfies it.

Flashcard 65: Which values in the set $\{-2,-1,0,1\}$ make the inequality $x<0$ true?

Answer: $-2$ and $-1$. Only negative values $-2$ and $-1$ are less than $0$.

Flashcard 66: Identify whether $x=1$ is a solution of $\frac{x+1}{2}=1$.

Answer: Yes, $x=1$ is a solution. $\frac{1+1}{2}=\frac{2}{2}=1$, which equals the right side.

Flashcard 67: Which value in $\{0,1,2,3\}$ makes $\frac{x}{2}=\frac{3}{2}$ true?

Answer: $3$. rac{3}{2}=rac{3}{2}, so $x=3$ satisfies it.

Flashcard 68: Which value in the set $\{2,3,4\}$ makes the equation $x+5=8$ true?

Answer: $3$. Since $3+5=8$, only $x=3$ satisfies the equation.