Question

1. solve for x

setup:
x=

Explanation:

Step1: Use tangent function

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. If we assume the angle opposite to the side of length $24$ and adjacent to the side of length $3(x + 2)$ is $\theta$, and assuming $\tan\theta = 1$ (if it is a 45 - 45 - 90 triangle, for simplicity, since no angle is given and we can consider the case where the two non - right angles are equal), then $\frac{24}{3(x + 2)}=1$.

Step2: Cross - multiply

Cross - multiplying the equation $\frac{24}{3(x + 2)}=1$ gives $24=3(x + 2)$.

Step3: Distribute on the right side

Expand $3(x + 2)$ to get $24 = 3x+6$.

Step4: Isolate the variable term

Subtract 6 from both sides: $24−6=3x$, so $18 = 3x$.

Step5: Solve for x

Divide both sides by 3: $x=\frac{18}{3}=6$.

Answer:

6