Answer :
To solve each of the given equations for [tex]\(x\)[/tex], let's go through them one by one:
1. Equation: [tex]\(2x + 3 = 71\)[/tex]
- Step 1: Subtract 3 from both sides to isolate the term with [tex]\(x\)[/tex].
[tex]\[
2x = 71 - 3
\][/tex]
- Step 2: Simplify the right-hand side.
[tex]\[
2x = 68
\][/tex]
- Step 3: Divide both sides by 2 to solve for [tex]\(x\)[/tex].
[tex]\[
x = \frac{68}{2} = 34
\][/tex]
2. Equation: [tex]\(2x + 3x = 71\)[/tex]
- Step 1: Combine like terms on the left-hand side.
[tex]\[
5x = 71
\][/tex]
- Step 2: Divide both sides by 5 to solve for [tex]\(x\)[/tex].
[tex]\[
x = \frac{71}{5} = 14.2
\][/tex]
3. Equation: [tex]\(11x - 6 = 71\)[/tex]
- Step 1: Add 6 to both sides to isolate the term with [tex]\(x\)[/tex].
[tex]\[
11x = 71 + 6
\][/tex]
- Step 2: Simplify the right-hand side.
[tex]\[
11x = 77
\][/tex]
- Step 3: Divide both sides by 11 to solve for [tex]\(x\)[/tex].
[tex]\[
x = \frac{77}{11} = 7
\][/tex]
4. Equation: [tex]\(7x - 6 = 71\)[/tex]
- Step 1: Add 6 to both sides to isolate the term with [tex]\(x\)[/tex].
[tex]\[
7x = 71 + 6
\][/tex]
- Step 2: Simplify the right-hand side.
[tex]\[
7x = 77
\][/tex]
- Step 3: Divide both sides by 7 to solve for [tex]\(x\)[/tex].
[tex]\[
x = \frac{77}{7} = 11
\][/tex]
Based on these solutions, the equations can be solved for [tex]\(x\)[/tex] as follows:
- [tex]\(x = 34\)[/tex] for the equation [tex]\(2x + 3 = 71\)[/tex]
- [tex]\(x = 14.2\)[/tex] for the equation [tex]\(2x + 3x = 71\)[/tex]
- [tex]\(x = 7\)[/tex] for the equation [tex]\(11x - 6 = 71\)[/tex]
- [tex]\(x = 11\)[/tex] for the equation [tex]\(7x - 6 = 71\)[/tex]
1. Equation: [tex]\(2x + 3 = 71\)[/tex]
- Step 1: Subtract 3 from both sides to isolate the term with [tex]\(x\)[/tex].
[tex]\[
2x = 71 - 3
\][/tex]
- Step 2: Simplify the right-hand side.
[tex]\[
2x = 68
\][/tex]
- Step 3: Divide both sides by 2 to solve for [tex]\(x\)[/tex].
[tex]\[
x = \frac{68}{2} = 34
\][/tex]
2. Equation: [tex]\(2x + 3x = 71\)[/tex]
- Step 1: Combine like terms on the left-hand side.
[tex]\[
5x = 71
\][/tex]
- Step 2: Divide both sides by 5 to solve for [tex]\(x\)[/tex].
[tex]\[
x = \frac{71}{5} = 14.2
\][/tex]
3. Equation: [tex]\(11x - 6 = 71\)[/tex]
- Step 1: Add 6 to both sides to isolate the term with [tex]\(x\)[/tex].
[tex]\[
11x = 71 + 6
\][/tex]
- Step 2: Simplify the right-hand side.
[tex]\[
11x = 77
\][/tex]
- Step 3: Divide both sides by 11 to solve for [tex]\(x\)[/tex].
[tex]\[
x = \frac{77}{11} = 7
\][/tex]
4. Equation: [tex]\(7x - 6 = 71\)[/tex]
- Step 1: Add 6 to both sides to isolate the term with [tex]\(x\)[/tex].
[tex]\[
7x = 71 + 6
\][/tex]
- Step 2: Simplify the right-hand side.
[tex]\[
7x = 77
\][/tex]
- Step 3: Divide both sides by 7 to solve for [tex]\(x\)[/tex].
[tex]\[
x = \frac{77}{7} = 11
\][/tex]
Based on these solutions, the equations can be solved for [tex]\(x\)[/tex] as follows:
- [tex]\(x = 34\)[/tex] for the equation [tex]\(2x + 3 = 71\)[/tex]
- [tex]\(x = 14.2\)[/tex] for the equation [tex]\(2x + 3x = 71\)[/tex]
- [tex]\(x = 7\)[/tex] for the equation [tex]\(11x - 6 = 71\)[/tex]
- [tex]\(x = 11\)[/tex] for the equation [tex]\(7x - 6 = 71\)[/tex]
