Question

find the value of x.
$10x - 80$
$8x + 7$

Explanation:

Step1: Identify equal segments

The figure shows that the segment labeled $10x - 80$ is composed of two congruent (triple-hashed) parts, and the segment labeled $8x + 7$ is congruent to one of those parts. This means $10x - 80$ is twice $8x + 7$.

Step2: Set up the equation

$$10x - 80 = 2(8x + 7)$$

Step3: Expand the right side

$$10x - 80 = 16x + 14$$

Step4: Isolate x terms

Subtract $10x$ from both sides:
$$-80 = 6x + 14$$

Step5: Isolate the constant term

Subtract 14 from both sides:
$$-94 = 6x$$

Step6: Solve for x

$$x = \frac{-94}{6} = -\frac{47}{3}$$

Answer:

$x = -\frac{47}{3}$