Question

1. given $\triangle stu \sim \triangle vtw$, solve for $x$.

remember
for problems 9 and 10, solve for $x$.

1. $2x + 4 + 3x = 14$
2. $3x - 7 - 5x = -16$

Explanation:

Step1: Set up similarity proportion

$\frac{ST}{VT} = \frac{SU}{VW}$
Substitute values: $\frac{x}{6} = \frac{22.5}{7.5}$

Step2: Simplify the right-hand side

$\frac{22.5}{7.5} = 3$, so $\frac{x}{6} = 3$

Step3: Solve for x

Multiply both sides by 6: $x = 3 \times 6$

Step4: Combine like terms (Q9)

$2x + 3x + 4 = 14 \implies 5x + 4 = 14$

Step5: Isolate x term (Q9)

$5x = 14 - 4 \implies 5x = 10$

Step6: Solve for x (Q9)

$x = \frac{10}{5} = 2$

Step7: Combine like terms (Q10)

$3x - 5x - 7 = -16 \implies -2x - 7 = -16$

Step8: Isolate x term (Q10)

$-2x = -16 + 7 \implies -2x = -9$

Step9: Solve for x (Q10)

$x = \frac{-9}{-2} = 4.5$

Answer:

Problem 8: $x = 18$
Problem 9: $x = 2$
Problem 10: $x = 4.5$