Question

Pls solve these problems!! THANK U!!!! :D

Answer 1

1) Sara's age = 19 years

2) x = 8

Explanation:

Solving algebraic equations:

1) Let Sara's age be x years.

Sara's aunt is 42 years older than Sara. So, we have to add 42 to the age of Sara.

Sara's aunt's age = x + 42

Five years ago,

Sara's age = x - 5

Aunt's age = (x + 42) - 5

= x + 37

Aunt's age = 4 times Sara's age

x + 37 = 4*(x - 5)

x + 37 = 4x - 4*5 {Distributive property}

x + 37 = 4x - 20

x + 37 + 20 = 4x {Add 20 to both sides}

x + 57 = 4x

57 = 4x - x {Subtract x from both sides}

57 = 3x

3x = 57

x = 57 ÷ 3 {Divide both sides by 3}

x = 19

Sara's age = 19 years

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2) To solve x,

• To open the parenthesis, multiply each term of
  `\left((3)/(8)x +(2)/(7)\right)` by (-1)

`\sf (2)/(7) + (5)/(8)x - \left((3)/(8)x+(2)/(7)\right)=2\\\\\\(2)/(7)+(5)/(8)x -(3)/(8)x - (2)/(7) =2\\\\\\`

`\sf \text{$(2)/(7)$ and $-(2)/(7)$ is 0}`

`\sf (5)/(8)x - (3)/(8)x=2\\\\\\`

`\sf (2)/(8)x = 2\\\\ (1)/(4)x=2\\\\\\`

Multiply both sides by 4,

`\sf 4 * (1)/(4)x = 2*4\\\\`

`\boxed{\bf x = 8}`