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Sagot :
Let's solve each equation step-by-step.
### First Equation:
[tex]\[ \frac{-10}{-14} = \frac{16x}{-14} \][/tex]
1. Simplify both sides:
[tex]\[ \frac{-10}{-14} \quad \text{simplifies to} \quad \frac{10}{14} = \frac{5}{7} \][/tex]
[tex]\[ \frac{16x}{-14} \quad \text{simplifies to} \quad \frac{-16x}{14} = -\frac{8x}{7} \][/tex]
Thus, the equation now is:
[tex]\[ \frac{5}{7} = -\frac{8x}{7} \][/tex]
2. To get rid of the denominators, multiply both sides by 7:
[tex]\[ 5 = -8x \][/tex]
3. Solve for [tex]\(x\)[/tex]:
[tex]\[ x = -\frac{5}{8} \][/tex]
4. Simplifying gives us:
[tex]\[ x = -0.625 \][/tex]
So, the solution to the first equation is:
[tex]\[ x = -0.625 \][/tex]
### Second Equation:
[tex]\[ 6x + 6(x + 6) = 96 \][/tex]
1. Distribute the 6 on the left side:
[tex]\[ 6x + 6x + 36 = 96 \][/tex]
2. Combine like terms:
[tex]\[ 12x + 36 = 96 \][/tex]
3. Subtract 36 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ 12x = 60 \][/tex]
4. Solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{60}{12} \][/tex]
[tex]\[ x = 5 \][/tex]
Thus, the solution to the second equation is:
[tex]\[ x = 5 \][/tex]
### Summary:
The solutions to the given system of equations are:
[tex]\[ x = -0.625 \quad \text{(from the first equation)} \][/tex]
[tex]\[ x = 5 \quad \text{(from the second equation)} \][/tex]
### First Equation:
[tex]\[ \frac{-10}{-14} = \frac{16x}{-14} \][/tex]
1. Simplify both sides:
[tex]\[ \frac{-10}{-14} \quad \text{simplifies to} \quad \frac{10}{14} = \frac{5}{7} \][/tex]
[tex]\[ \frac{16x}{-14} \quad \text{simplifies to} \quad \frac{-16x}{14} = -\frac{8x}{7} \][/tex]
Thus, the equation now is:
[tex]\[ \frac{5}{7} = -\frac{8x}{7} \][/tex]
2. To get rid of the denominators, multiply both sides by 7:
[tex]\[ 5 = -8x \][/tex]
3. Solve for [tex]\(x\)[/tex]:
[tex]\[ x = -\frac{5}{8} \][/tex]
4. Simplifying gives us:
[tex]\[ x = -0.625 \][/tex]
So, the solution to the first equation is:
[tex]\[ x = -0.625 \][/tex]
### Second Equation:
[tex]\[ 6x + 6(x + 6) = 96 \][/tex]
1. Distribute the 6 on the left side:
[tex]\[ 6x + 6x + 36 = 96 \][/tex]
2. Combine like terms:
[tex]\[ 12x + 36 = 96 \][/tex]
3. Subtract 36 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ 12x = 60 \][/tex]
4. Solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{60}{12} \][/tex]
[tex]\[ x = 5 \][/tex]
Thus, the solution to the second equation is:
[tex]\[ x = 5 \][/tex]
### Summary:
The solutions to the given system of equations are:
[tex]\[ x = -0.625 \quad \text{(from the first equation)} \][/tex]
[tex]\[ x = 5 \quad \text{(from the second equation)} \][/tex]
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