Sure! Let's go through the equations one by one and solve each in a detailed, step-by-step manner.
### Question 6: Solve the equation [tex]\( 7x = 6 + 5x \)[/tex]
1. Start with the given equation:
[tex]\[
7x = 6 + 5x
\][/tex]
2. Subtract [tex]\( 5x \)[/tex] from both sides of the equation to isolate the variable term on one side:
[tex]\[
7x - 5x = 6
\][/tex]
3. Simplify the left-hand side:
[tex]\[
2x = 6
\][/tex]
4. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{6}{2} = 3
\][/tex]
Answer: [tex]\( x = 3 \)[/tex]
### Question 7: Solve the equation [tex]\( 30 = 4x + 6 \)[/tex]
1. Start with the given equation:
[tex]\[
30 = 4x + 6
\][/tex]
2. Subtract 6 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
30 - 6 = 4x
\][/tex]
3. Simplify the left-hand side:
[tex]\[
24 = 4x
\][/tex]
4. Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{24}{4} = 6
\][/tex]
Answer: [tex]\( x = 6 \)[/tex]
### Question 8: Solve the equation [tex]\( 2(x + 4) = 16 \)[/tex]
1. Start with the given equation:
[tex]\[
2(x + 4) = 16
\][/tex]
2. Divide both sides by 2 to simplify:
[tex]\[
x + 4 = \frac{16}{2}
\][/tex]
3. Simplify the right-hand side:
[tex]\[
x + 4 = 8
\][/tex]
4. Subtract 4 from both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 8 - 4 = 4
\][/tex]
Answer: [tex]\( x = 4 \)[/tex]
### Question 9: Solve the equation [tex]\( 7 + 5x = 3x + 13 \)[/tex]
1. Start with the given equation:
[tex]\[
7 + 5x = 3x + 13
\][/tex]
2. Subtract [tex]\( 3x \)[/tex] from both sides to isolate the [tex]\( x \)[/tex] terms on one side:
[tex]\[
7 + 5x - 3x = 13
\][/tex]
3. Simplify:
[tex]\[
7 + 2x = 13
\][/tex]
4. Subtract 7 from both sides:
[tex]\[
2x = 13 - 7
\][/tex]
5. Simplify the right-hand side:
[tex]\[
2x = 6
\][/tex]
6. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{6}{2} = 3
\][/tex]
Answer: [tex]\( x = 3 \)[/tex]
In conclusion, the solutions to the equations are:
1. [tex]\( x = 3 \)[/tex]
2. [tex]\( x = 6 \)[/tex]
3. [tex]\( x = 4 \)[/tex]
4. [tex]\( x = 3 \)[/tex]
