Certainly! Let me provide you with a detailed, step-by-step explanation along with justifications for solving the given equation [tex]\( 5(2x+1)=2(4x-7)+3 \)[/tex].
3. Combine like terms on the right side: [tex]\[
10x + 5 = 8x - 11
\][/tex] Justification: Combine like terms.
4. Subtract [tex]\(8x\)[/tex] from both sides of the equation to start isolating [tex]\(x\)[/tex]: [tex]\[
10x - 8x + 5 = -11
\][/tex] Simplifying, we get: [tex]\[
2x + 5 = -11
\][/tex] Justification: Addition property of equality (subtracting [tex]\(8x\)[/tex] from both sides).
5. Next, subtract [tex]\(5\)[/tex] from both sides to further isolate [tex]\(x\)[/tex]: [tex]\[
2x + 5 - 5 = -11 - 5
\][/tex] Simplifying, we get: [tex]\[
2x = -16
\][/tex] Justification: Addition property of equality (subtracting [tex]\(5\)[/tex] from both sides).
6. Finally, divide both sides by [tex]\(2\)[/tex] to solve for [tex]\(x\)[/tex]: [tex]\[
x = \frac{-16}{2}
\][/tex] Simplifying, we get: [tex]\[
x = -8
\][/tex] Justification: Multiplication property of equality (dividing both sides by [tex]\(2\)[/tex]).
Thus, the solution to the equation [tex]\(5(2x+1) = 2(4x-7) + 3\)[/tex] is [tex]\(x = -8\)[/tex].
