Question

Solve the following equation if there is no solution enter no solution|x+3| + 7=2

Answer 1

The given equation:

`|x+3|+7=2`

can be simplified as follow

Step 1: collect like terms

`\begin{gathered} |x+3|=2-7 \\ |x+3|=-5 \end{gathered}`

Step 2: Sice the equation involves absolute values,

assume two cases

case 1: take the result of the left-hand side to be positive so that

`x+3=-5`

Then

`\begin{gathered} x=-5-3 \\ x=-8 \end{gathered}`

Case 2: take the result of the left-hand side to be negative so that

`\begin{gathered} x+3=-(-5) \\ x+3=5 \end{gathered}`

then

`\begin{gathered} x=5-3 \\ x=2 \end{gathered}`

Step 3: Check if the values of x obtained in step 2 satisfy the original equation

when x=-8

`\begin{gathered} |x+3+7=2 \\ |-8+3|+7 \\ |-5|+7=5+7 \\ \sin ce \\ 5+7\\e2 \\ i\mathrm{}e \\ 12\\e2 \end{gathered}`

Then x=-8 is not a solution

Similarly

when x=2

`\begin{gathered} |x+3|+7=2 \\ |2+3|+7=|5|+7 \\ 5+7\\e2 \\ i\mathrm{}e \\ 12\\e2 \end{gathered}`

Also, x=2 is not a solution,

therefore

The equation has no solution