Understand Solving Equations and Inequalities - 6th Grade Math
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What does it mean for a value to be a solution of an inequality?
What does it mean for a value to be a solution of an inequality?
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A value that makes the inequality true when substituted. Substitution verifies if the inequality holds true.
A value that makes the inequality true when substituted. Substitution verifies if the inequality holds true.
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Which value in the set ${0, 1, 2}$ makes $3x = 6$ true?
Which value in the set ${0, 1, 2}$ makes $3x = 6$ true?
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$2$. Substitute: $3(2) = 6$ is true.
$2$. Substitute: $3(2) = 6$ is true.
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Which values in the set ${-2,-1,0,1}$ make the inequality $x<0$ true?
Which values in the set ${-2,-1,0,1}$ make the inequality $x<0$ true?
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$-2$ and $-1$. Only negative values $-2$ and $-1$ are less than $0$.
$-2$ and $-1$. Only negative values $-2$ and $-1$ are less than $0$.
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Which values in the set ${0,1,2,3}$ make the inequality $3-x\ge 2$ true?
Which values in the set ${0,1,2,3}$ make the inequality $3-x\ge 2$ true?
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$0$ and $1$. Since $3-0=3ge 2$ and $3-1=2ge 2$, both satisfy.
$0$ and $1$. Since $3-0=3ge 2$ and $3-1=2ge 2$, both satisfy.
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Which value in the set ${0,1,2,3}$ makes the equation $4(x-1)=8$ true?
Which value in the set ${0,1,2,3}$ makes the equation $4(x-1)=8$ true?
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$3$. Since $4(3-1)=4(2)=8$, only $x=3$ satisfies.
$3$. Since $4(3-1)=4(2)=8$, only $x=3$ satisfies.
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Which value in the set ${1,2,3,4}$ makes the equation $2(x+1)=10$ true?
Which value in the set ${1,2,3,4}$ makes the equation $2(x+1)=10$ true?
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$4$. Since $2(4+1)=2(5)=10$, only $x=4$ satisfies.
$4$. Since $2(4+1)=2(5)=10$, only $x=4$ satisfies.
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Which value in the set ${-1,0,1,2}$ makes the equation $5-x=4$ true?
Which value in the set ${-1,0,1,2}$ makes the equation $5-x=4$ true?
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$1$. Since $5-1=4$, only $x=1$ satisfies the equation.
$1$. Since $5-1=4$, only $x=1$ satisfies the equation.
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What is the first step to check whether $x=4$ is a solution of $2x+1=9$?
What is the first step to check whether $x=4$ is a solution of $2x+1=9$?
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Substitute $4$ for $x$ in $2x+1$ and compare to $9$. Substitution checks if the value satisfies the equation.
Substitute $4$ for $x$ in $2x+1$ and compare to $9$. Substitution checks if the value satisfies the equation.
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Which value in the set ${2,3,4}$ makes the equation $x+5=8$ true?
Which value in the set ${2,3,4}$ makes the equation $x+5=8$ true?
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$3$. Since $3+5=8$, only $x=3$ satisfies the equation.
$3$. Since $3+5=8$, only $x=3$ satisfies the equation.
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Which value in the set ${2,3,4}$ makes the equation $\frac{x}{2}=2$ true?
Which value in the set ${2,3,4}$ makes the equation $\frac{x}{2}=2$ true?
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$4$. Since $ rac{4}{2}=2$, only $x=4$ satisfies the equation.
$4$. Since $ rac{4}{2}=2$, only $x=4$ satisfies the equation.
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Which value in the set ${1,2,3}$ makes the equation $2x+1=7$ true?
Which value in the set ${1,2,3}$ makes the equation $2x+1=7$ true?
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$3$. Since $2(3)+1=7$, only $x=3$ satisfies the equation.
$3$. Since $2(3)+1=7$, only $x=3$ satisfies the equation.
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Which value in the set ${1,2,3,4}$ makes the equation $10-x=6$ true?
Which value in the set ${1,2,3,4}$ makes the equation $10-x=6$ true?
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$4$. Since $10-4=6$, only $x=4$ satisfies the equation.
$4$. Since $10-4=6$, only $x=4$ satisfies the equation.
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What does it mean for a value to be a solution of the equation $x+3=10$?
What does it mean for a value to be a solution of the equation $x+3=10$?
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It makes the equation true when substituted for $x$. A solution satisfies the equation when plugged in for the variable.
It makes the equation true when substituted for $x$. A solution satisfies the equation when plugged in for the variable.
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Which value in the set {0,1,2} makes the equation $3x=6$ true?
Which value in the set {0,1,2} makes the equation $3x=6$ true?
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$2$. Since $3(2)=6$, only $x=2$ satisfies the equation.
$2$. Since $3(2)=6$, only $x=2$ satisfies the equation.
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Which statement correctly describes checking $x=2$ in $x+1=4$?
Which statement correctly describes checking $x=2$ in $x+1=4$?
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Substitute: $2+1=3$, so $x=2$ is not a solution. Shows substitution yields $3
eq 4$, proving it's not a solution.
Substitute: $2+1=3$, so $x=2$ is not a solution. Shows substitution yields $3 eq 4$, proving it's not a solution.
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Which value in the set ${1,2,3}$ makes the inequality $x+2>4$ true?
Which value in the set ${1,2,3}$ makes the inequality $x+2>4$ true?
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$3$. Since $3+2=5>4$, only $x=3$ satisfies the inequality.
$3$. Since $3+2=5>4$, only $x=3$ satisfies the inequality.
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Which value in the set ${3,4,5}$ makes the equation $\frac{x}{5}=1$ true?
Which value in the set ${3,4,5}$ makes the equation $\frac{x}{5}=1$ true?
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$5$. Since $ rac{5}{5}=1$, only $x=5$ satisfies the equation.
$5$. Since $ rac{5}{5}=1$, only $x=5$ satisfies the equation.
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Which values in the set ${0,1,2,3}$ make the inequality $x\le 2$ true?
Which values in the set ${0,1,2,3}$ make the inequality $x\le 2$ true?
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$0,1,2$. Values $0$, $1$, and $2$ are all less than or equal to $2$.
$0,1,2$. Values $0$, $1$, and $2$ are all less than or equal to $2$.
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Which values in the set ${1,2,3,4}$ make the inequality $2x \ge 6$ true?
Which values in the set ${1,2,3,4}$ make the inequality $2x \ge 6$ true?
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$3$ and $4$. Since $2(3)=6$ and $2(4)=8$, both are $\ge 6$.
$3$ and $4$. Since $2(3)=6$ and $2(4)=8$, both are $\ge 6$.
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Which values in ${-1,0,1,2}$ satisfy $x\ge 1$?
Which values in ${-1,0,1,2}$ satisfy $x\ge 1$?
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${1,2}$. Values greater than or equal to 1 are 1 and 2.
${1,2}$. Values greater than or equal to 1 are 1 and 2.
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What is substitution when checking a possible solution for $x$?
What is substitution when checking a possible solution for $x$?
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Replace $x$ with the given value and evaluate both sides. Substitution means plugging in a value for the variable.
Replace $x$ with the given value and evaluate both sides. Substitution means plugging in a value for the variable.
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Which value in ${0,1,2,3}$ makes $\frac{x}{2}=\frac{3}{2}$ true?
Which value in ${0,1,2,3}$ makes $\frac{x}{2}=\frac{3}{2}$ true?
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$3$. $ rac{3}{2}= rac{3}{2}$, so $x=3$ satisfies it.
$3$. $ rac{3}{2}= rac{3}{2}$, so $x=3$ satisfies it.
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Which values are considered when the problem gives a specified set $S$?
Which values are considered when the problem gives a specified set $S$?
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Only values in $S$ can be solutions. Solutions must come from the given set.
Only values in $S$ can be solutions. Solutions must come from the given set.
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Identify whether $x=0$ is a solution of $7x-4=3$.
Identify whether $x=0$ is a solution of $7x-4=3$.
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No, $x=0$ is not a solution. $7(0)-4=0-4=-4$, which doesn't equal $3$.
No, $x=0$ is not a solution. $7(0)-4=0-4=-4$, which doesn't equal $3$.
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Which values in ${0,1,2,3}$ make $x^2=4$ true?
Which values in ${0,1,2,3}$ make $x^2=4$ true?
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$x=2$ only. Only $2^2=4$; the other values squared don't equal $4$.
$x=2$ only. Only $2^2=4$; the other values squared don't equal $4$.
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