Expressions, Equations, and Relationships>Modeling and Solving One-Variable, Two-Step Equations and Inequalities(TEKS.Math.7.11.A)
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Texas 7th Grade Math › Expressions, Equations, and Relationships>Modeling and Solving One-Variable, Two-Step Equations and Inequalities(TEKS.Math.7.11.A)
Solve: $5x - 8 = 27$. Which value of $x$ makes this equation true?
5
6
7
8
Explanation
Add 8 to both sides to undo the subtraction: $5x = 35$. Then divide both sides by 5: $x = 7$. Check: $5(7) - 8 = 35 - 8 = 27$, which is true.
Solve the inequality: $3y + 12 \le 30$. What is the solution for $y$?
$y \le 6$
$y \ge 6$
$y \le -6$
$y < 6$
Explanation
Subtract 12 from both sides: $3y \le 18$. Divide both sides by 3: $y \le 6$. No inequality flip is needed because we divided by a positive number. Check with $y=6$: $3(6)+12=18+12=30$, which satisfies $\le 30$.
Find $x$: $2(x + 4) = 18$. What is the solution?
14
9
-5
5
Explanation
Undo the multiplication first by dividing both sides by 2: $x+4=9$. Then undo the addition by subtracting 4: $x=5$. Check: $2(5+4)=2\cdot9=18$, true.
Solve the inequality: $-6z - 9 > 15$. What is the solution for $z$?
$z > -4$
$z < -4$
$z \le -4$
$z < 4$
Explanation
Add 9 to both sides: $-6z > 24$. Divide both sides by $-6$ and reverse the inequality: $z < -4$. Check with $z=-5$: $-6(-5)-9=30-9=21$, and $21>15$ is true. Note $z=-4$ gives $15$, which is not greater than 15.
Solve: $\frac{x}{3} + 5 = 11$. What is the value of $x$?
18
6
2
-18
Explanation
Subtract 5 from both sides: $\frac{x}{3}=6$. Multiply both sides by 3: $x=18$. Check: $\frac{18}{3}+5=6+5=11$, true.