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Sagot :
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]
### 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]
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