Question

What is the soution to the equation 1/2 x + 3 = 2/3 x + 1

a.1/3
b.2/3
c.2
d.12

Answer 1

• Answer:

`\boxed{\bold{x=12}}`

• Explanation:

• Subtract 3 from both sides

`\bold{(1)/(2)x+3-3=(2)/(3)x+1-3}`

• Simplify

`\bold{(1)/(2)x=(2)/(3)x-2}`

• Subtract
  `\bold{(2)/(3)x }` from both sides

`\bold{(1)/(2)x-(2)/(3)x=(2)/(3)x-2-(2)/(3)x}`

• Simplify

`\bold{-(1)/(6)x=-2}`

• Multiply both sides by -6

`\bold{\left(-(1)/(6)x\right)\left(-6\right)=\left(-2\right)\left(-6\right)}`

• Simplify

`\bold{x=12}`

Answer 2

d

Explanation:

To eliminate the fractions in the equation multiply all term on both sides by the lowest common multiple of 2 and 3, that is 6

3x + 18 = 4x + 6 ← equation with no fractions

Subtract 4x from both sides

- x + 18 = 6 ( subtract 18 from both sides )

- x = - 12 ( multiply both sides by - 1 )

x = 12 → d