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Solve the following equations:

i) [tex]5x - 3 = 3x + 7[/tex]

ii) [tex]4x + 2 = 2x - 6[/tex]

iii) [tex]4x + 5 = 13[/tex]


Sagot :

Let's solve each of the equations step by step.

### i) [tex]\(5x - 3 = 3x + 7\)[/tex]

1. Move the [tex]\(3x\)[/tex] term from the right side to the left side to isolate the variable terms on one side:
[tex]\[ 5x - 3 - 3x = 7 \][/tex]
2. Simplify the left side:
[tex]\[ 2x - 3 = 7 \][/tex]
3. Move the constant term [tex]\(-3\)[/tex] from the left side to the right side to isolate the variable term:
[tex]\[ 2x = 7 + 3 \][/tex]
4. Simplify the right side:
[tex]\[ 2x = 10 \][/tex]
5. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{10}{2} \][/tex]
[tex]\[ x = 5 \][/tex]

So, the solution is [tex]\( x = 5 \)[/tex].

### ii) [tex]\(4x + 2 = 2x - 6\)[/tex]

1. Move the [tex]\(2x\)[/tex] term from the right side to the left side to isolate the variable terms on one side:
[tex]\[ 4x + 2 - 2x = -6 \][/tex]
2. Simplify the left side:
[tex]\[ 2x + 2 = -6 \][/tex]
3. Move the constant term [tex]\(2\)[/tex] from the left side to the right side to isolate the variable term:
[tex]\[ 2x = -6 - 2 \][/tex]
4. Simplify the right side:
[tex]\[ 2x = -8 \][/tex]
5. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-8}{2} \][/tex]
[tex]\[ x = -4 \][/tex]

So, the solution is [tex]\( x = -4 \)[/tex].

### iii) [tex]\(4x + 5 = 13\)[/tex]

1. Move the constant term [tex]\(5\)[/tex] from the left side to the right side to isolate the variable term:
[tex]\[ 4x + 5 - 5 = 13 - 5 \][/tex]
2. Simplify both sides:
[tex]\[ 4x = 8 \][/tex]
3. Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{8}{4} \][/tex]
[tex]\[ x = 2 \][/tex]

So, the solution is [tex]\( x = 2 \)[/tex].

### Summary
The solutions for the given equations are:
i) [tex]\( x = 5 \)[/tex]
ii) [tex]\( x = -4 \)[/tex]
iii) [tex]\( x = 2 \)[/tex]
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