Question

stion 2
lve the equation $3(x + 7) - 2 = 10x - 16$ for $x$.
u must show your work for full credit

Explanation:

Step1: Expand the left side

First, we expand \( 3(x + 7) \) using the distributive property \( a(b + c)=ab+ac \). So \( 3(x + 7)=3x+21 \). Then the left side of the equation \( 3(x + 7)-2 \) becomes \( 3x + 21-2 \). Simplifying \( 21-2 \) gives \( 3x+19 \). So the equation is now \( 3x + 19=10x-16 \).

Step2: Move all x terms to one side

Subtract \( 3x \) from both sides to get all the \( x \) terms on the right side. \( 3x+19 - 3x=10x-16-3x \), which simplifies to \( 19 = 7x-16 \).

Step3: Solve for x

Add 16 to both sides to isolate the term with \( x \). \( 19 + 16=7x-16 + 16 \), so \( 35 = 7x \). Then divide both sides by 7: \( \frac{35}{7}=\frac{7x}{7} \), which gives \( x = 5 \).

Answer:

\( x = 5 \)