Question

equations with variables on both sides, evaluate each equation W - 20 = 6w 2n -5 = 7n 3 (f + 5)= 13+5f2(6c + 1 ) = 4 (c - 5) - 27 (a - 2) = 5( a + 2 )

Answer 1

(1). The given expression :

`w-20=6w`

Simplify :

`\begin{gathered} w-20=6w \\ subtract\text{ w on both side of equation} \\ w-w-20=6w-w \\ 5w=-20 \\ \text{divide both side by 5} \\ (5w)/(5)=(-20)/(5) \\ w=(-4) \end{gathered}`

Answer : w = (-4)

(2). the given expression :

`\begin{gathered} 2n-5=7n \\ subtract\text{ 2n from both side of the equation} \\ 2n-2n-5=7n-2n \\ -5=5n \\ \text{Divide both side by 5,} \\ (-5)/(5)=(5n)/(5) \\ n=-1 \end{gathered}`

Answer : n = -1

(3). The given expression :

`\begin{gathered} 3\text{ (f+5)=13+5f} \\ \text{simplify the brackets} \\ 3f+15=13+5f \\ \text{subtract 3f from both side} \\ 3f-3f+15=13+5f-3f \\ 15=13+2f \\ \text{subtract 13 from both side} \\ 15-13=13-13+2f \\ 2f=2 \\ f=1 \end{gathered}`

Answer : f=1

(4). The given expression is :

`\begin{gathered} 2(6c+1)=4(c-5)-2_{} \\ \text{Simplify the brackets} \\ 12c+2=4c-20-2 \\ \text{subtract 4c from both side and simplify} \\ 12c-4c+2=4c-4c-22 \\ 8c+2=-22 \\ \text{subtract 2 f rom both side} \\ 8c+2-2=-22-2 \\ 8c=-24 \\ \text{Divide both side by 8} \\ (8c)/(8)=(-24)/(8) \\ c=(-3) \end{gathered}`

Answer : c = -3

(5). The given expression :

`\begin{gathered} 7(a-2)=5(a+2) \\ \text{simplify the brackets} \\ 7a-14=5a+10 \\ \text{Subtract 5a on both side} \\ 7a-14-5a=5a-5a+10 \\ 2a-14=10 \\ \text{add 14 on both side} \\ 2a-14+14=10+14 \\ 2a=24 \\ Divide\text{ both side by 2,} \\ (2a)/(2)=(24)/(2) \\ a=12 \end{gathered}`

Answer : a=12