Certainly! Let's solve each equation step-by-step.
Question 21: Solve the equation [tex]\(6x + 10 = -14\)[/tex]
1. Subtract 10 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
6x + 10 - 10 = -14 - 10
\][/tex]
This simplifies to:
[tex]\[
6x = -24
\][/tex]
2. Divide both sides by 6 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-24}{6}
\][/tex]
This gives:
[tex]\[
x = -4
\][/tex]
So, the solution to the first equation is [tex]\(x = -4\)[/tex].
Question 22: Solve the equation [tex]\(7x - 17 = 6x - 13\)[/tex]
1. Subtract [tex]\(6x\)[/tex] from both sides to get all the [tex]\(x\)[/tex]-terms on one side:
[tex]\[
7x - 6x - 17 = 6x - 6x - 13
\][/tex]
This simplifies to:
[tex]\[
x - 17 = -13
\][/tex]
2. Add 17 to both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
x - 17 + 17 = -13 + 17
\][/tex]
This gives:
[tex]\[
x = 4
\][/tex]
So, the solution to the second equation is [tex]\(x = 4\)[/tex].
In conclusion, the solutions to the given equations are:
- For [tex]\(6x + 10 = -14\)[/tex]: [tex]\(x = -4\)[/tex]
- For [tex]\(7x - 17 = 6x - 13\)[/tex]: [tex]\(x = 4\)[/tex]
