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Solve the following equations with brackets:

[tex]\[
\begin{array}{l}
1. \ 2(x-4) = 3(x+2) \\
2. \ -3(x-1) = 2(x-4) \\
3. \ -3(x+2) - 3x = 3(x+1) \\
4. \ -3(x+2) = 3(x+1)
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
Certainly, let's solve each of these equations step-by-step.

### 1. Solve [tex]\(2(x-4)=3(x+2)\)[/tex]

Equation: [tex]\(2(x-4)=3(x+2)\)[/tex]

Step-by-Step:
1. Distribute the constants within the brackets:
[tex]\[ 2x - 8 = 3x + 6 \][/tex]
2. Isolate the terms involving [tex]\( x \)[/tex] on one side:
[tex]\[ 2x - 3x = 6 + 8 \][/tex]
3. Simplify the equation:
[tex]\[ -x = 14 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = -14 \][/tex]

### 2. Solve [tex]\(-3(x-1)=2(x-4)\)[/tex]

Equation: [tex]\(-3(x-1)=2(x-4)\)[/tex]

Step-by-Step:
1. Distribute the constants within the brackets:
[tex]\[ -3x + 3 = 2x - 8 \][/tex]
2. Isolate the terms involving [tex]\( x \)[/tex] on one side:
[tex]\[ -3x - 2x = -8 - 3 \][/tex]
3. Simplify the equation:
[tex]\[ -5x = -11 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{11}{5} \][/tex]

### 3. Solve [tex]\(-3(x+2)-3x=3(x+1)\)[/tex]

Equation: [tex]\(-3(x+2)-3x=3(x+1)\)[/tex]

Step-by-Step:
1. Distribute the constants within the brackets:
[tex]\[ -3x - 6 - 3x = 3x + 3 \][/tex]
2. Combine the [tex]\( x \)[/tex] terms on the left-hand side:
[tex]\[ -6x - 6 = 3x + 3 \][/tex]
3. Isolate the terms involving [tex]\( x \)[/tex] on one side:
[tex]\[ -6x - 3x = 3 + 6 \][/tex]
4. Simplify the equation:
[tex]\[ -9x = 9 \][/tex]
5. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = -1 \][/tex]

### 4. Solve [tex]\(-3(x+2)=3(x+1)\)[/tex]

Equation: [tex]\(-3(x+2)=3(x+1)\)[/tex]

Step-by-Step:
1. Distribute the constants within the brackets:
[tex]\[ -3x - 6 = 3x + 3 \][/tex]
2. Isolate the terms involving [tex]\( x \)[/tex] on one side:
[tex]\[ -3x - 3x = 3 + 6 \][/tex]
3. Simplify the equation:
[tex]\[ -6x = 9 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = -\frac{3}{2} \][/tex]

### Summary of Solutions

- For the first equation [tex]\(2(x-4)=3(x+2)\)[/tex], [tex]\(x = -14\)[/tex].
- For the second equation [tex]\(-3(x-1)=2(x-4)\)[/tex], [tex]\(x = \frac{11}{5}\)[/tex].
- For the third equation [tex]\(-3(x+2)-3x=3(x+1)\)[/tex], [tex]\(x = -1\)[/tex].
- For the fourth equation [tex]\(-3(x+2)=3(x+1)\)[/tex], [tex]\(x = -\frac{3}{2}\)[/tex].
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