To solve the equation [tex]\(4x - 5 + 2x + 10 = 3x - 3\)[/tex], follow these step-by-step instructions:
1. Combine like terms on the left side of the equation:
Combine the [tex]\(x\)[/tex]-terms and the constant terms:
[tex]\[
4x + 2x - 5 + 10 = 6x + 5
\][/tex]
So the left side of the equation is now:
[tex]\[
6x + 5
\][/tex]
2. Rewrite the equation with the simplified left side:
[tex]\[
6x + 5 = 3x - 3
\][/tex]
3. Move all [tex]\(x\)[/tex]-terms to one side of the equation and constant terms to the other side:
Subtract [tex]\(3x\)[/tex] from both sides to get the [tex]\(x\)[/tex]-terms on one side:
[tex]\[
6x - 3x + 5 = -3
\][/tex]
Simplify this to:
[tex]\[
3x + 5 = -3
\][/tex]
4. Isolate the [tex]\(x\)[/tex]-term:
Subtract 5 from both sides of the equation to move the constants to the right side:
[tex]\[
3x + 5 - 5 = -3 - 5
\][/tex]
Simplify this to:
[tex]\[
3x = -8
\][/tex]
5. Solve for [tex]\(x\)[/tex]:
Divide both sides by 3 to isolate [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-8}{3}
\][/tex]
So, the solution to the equation is [tex]\( x = -\frac{8}{3} \)[/tex].
Therefore, the correct answer is:
(B) [tex]\( x = -\frac{8}{3} \)[/tex]
