Question

linear equations w/ distribution (lev 3)
score: 1/6 penalty: none
question
solve for ( x ):
( 3 - 5(-3x + 1) + 8x = -2x + 5 )
answer attempt 1 out of 2
( x = )
submit answer

Explanation:

Step1: Distribute the -5

First, we distribute the -5 into the parentheses \(-5(-3x + 1)\). Using the distributive property \(a(b + c)=ab+ac\), we get:
\(3 + 15x - 5 + 8x = -2x + 5\)

Step2: Combine like terms on the left

Combine the constant terms (3 and -5) and the \(x\)-terms (15x and 8x) on the left side:
\((3 - 5)+(15x + 8x)= -2x + 5\)
\(-2 + 23x = -2x + 5\)

Step3: Add 2x to both sides

To get all the \(x\)-terms on one side, we add \(2x\) to both sides of the equation:
\(-2 + 23x + 2x = -2x + 2x + 5\)
\(-2 + 25x = 5\)

Step4: Add 2 to both sides

Now, we add 2 to both sides to isolate the term with \(x\):
\(-2 + 2 + 25x = 5 + 2\)
\(25x = 7\)

Step5: Divide by 25

Finally, we divide both sides by 25 to solve for \(x\):
\(x=\frac{7}{25}\)

Answer:

\(\frac{7}{25}\)