Question

thad solved the equation as shown. which statement is true about thads work?
solve: ( 3(x + 5)=7x + 15 - 3x )
( 3x + 15 = 4x + 15 )
( x = 0 )
a thad solved the equation incorrectly.
b thad solved the equation correctly and there is no solution.
c thad solved the equation correctly and there is one solution.
d thad solved the equation correctly and there are infinitely many solutions.

Explanation:

Step1: Simplify the right - hand side

First, we simplify the right - hand side of the equation \(7x + 15-3x\). Combining like terms, \(7x-3x=4x\), so the equation becomes \(3(x + 5)=4x + 15\).

Step2: Expand the left - hand side

Using the distributive property \(a(b + c)=ab+ac\), for \(3(x + 5)\), we get \(3x+15\). So now the equation is \(3x + 15=4x + 15\).

Step3: Solve for \(x\)

Subtract \(3x\) from both sides: \(3x+15 - 3x=4x + 15-3x\), which simplifies to \(15=x + 15\). Then subtract 15 from both sides: \(15-15=x + 15-15\), so \(x = 0\). Wait, but let's check again. Wait, if we start from \(3x+15 = 4x + 15\), subtract \(3x\) from both sides: \(15=x + 15\), then subtract 15: \(x=0\). But let's substitute \(x = 0\) back into the original equation. Left - hand side: \(3(0 + 5)=15\). Right - hand side: \(7(0)+15-3(0)=15\). So \(x = 0\) is a solution. But wait, let's re - examine the steps. Wait, when we have \(3x+15=4x + 15\), if we subtract \(3x\) and 15 from both sides, we get \(0=x\), so \(x = 0\) is a valid solution. So Thad solved the equation correctly and there is one solution.

Answer:

C. Thad solved the equation correctly and there is one solution.