Sure! Let's solve each equation step by step:
### Equation 1: [tex]\(7x = 6 + 5x\)[/tex]
1. Subtract [tex]\(5x\)[/tex] from both sides to isolate the terms with [tex]\(x\)[/tex] on one side:
[tex]\[
7x - 5x = 6 + 5x - 5x
\][/tex]
Which simplifies to:
[tex]\[
2x = 6
\][/tex]
2. Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{6}{2} = 3
\][/tex]
So, the value of [tex]\(x\)[/tex] for the first equation is [tex]\(\boxed{3}\)[/tex].
### Equation 2: [tex]\(30 = 4x + 6\)[/tex]
1. Subtract 6 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
30 - 6 = 4x + 6 - 6
\][/tex]
Which simplifies to:
[tex]\[
24 = 4x
\][/tex]
2. Divide both sides by 4 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{24}{4} = 6
\][/tex]
So, the value of [tex]\(x\)[/tex] for the second equation is [tex]\(\boxed{6}\)[/tex].
### Equation 3: [tex]\(2(x + 4) = 16\)[/tex]
1. Distribute the 2 on the left side:
[tex]\[
2x + 8 = 16
\][/tex]
2. Subtract 8 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
2x + 8 - 8 = 16 - 8
\][/tex]
Which simplifies to:
[tex]\[
2x = 8
\][/tex]
3. Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{8}{2} = 4
\][/tex]
So, the value of [tex]\(x\)[/tex] for the third equation is [tex]\(\boxed{4}\)[/tex].
### Equation 4: [tex]\(7 + 5x = 3x + 13\)[/tex]
1. Subtract [tex]\(3x\)[/tex] from both sides to isolate the terms with [tex]\(x\)[/tex] on one side:
[tex]\[
7 + 5x - 3x = 3x + 13 - 3x
\][/tex]
Which simplifies to:
[tex]\[
7 + 2x = 13
\][/tex]
2. Subtract 7 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
7 + 2x - 7 = 13 - 7
\][/tex]
Which simplifies to:
[tex]\[
2x = 6
\][/tex]
3. Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{6}{2} = 3
\][/tex]
So, the value of [tex]\(x\)[/tex] for the fourth equation is [tex]\(\boxed{3}\)[/tex].
In summary, the values of [tex]\(x\)[/tex] for the given equations are:
1. [tex]\(x = 3\)[/tex]
2. [tex]\(x = 6\)[/tex]
3. [tex]\(x = 4\)[/tex]
4. [tex]\(x = 3\)[/tex]
