Question

The solution setfor the equation modulus X + 2 is less than or equal to 5 ?

Answer 1

Answer:

The solution set for the given equation is

$\displaystyle{\boxed{\pink{\sf\:x\:\in\:\{\:-\:7,\:-\:6,\:-\:5,\:-\:4,\:-\:3,\:-\:2,\:-\:1,\:0,\:1,\:2,\:3\:\}\:}}}$

Step-by-step-explanation:

The given inequality is

$\displaystyle{\sf\:|\:x\:+\:2\:|\:\leq\:5}$

We have to find the value of x.

Now, we know that,

If $\displaystyle{\sf\:|\:x\:|\:\leq\:a}$, then

$\displaystyle{\boxed{\green{\sf\:x\:\leq\:a}}\sf\:\quad\:OR\:\quad\:\boxed{\green{\sf\:x\:\geq\:-\:a}}}$

Now,

$\displaystyle{\sf\:|\:x\:+\:2\:|\:\leq\:5}$

$\displaystyle{\implies\sf\:x\:+\:2\:\leq\:5\:\quad\:OR\:\quad\:x\:+\:2\:\geq\:-\:5}$

$\displaystyle{\implies\sf\:x\:\leq\:5\:-\:2\:\quad\:OR\:\quad\:x\:\geq\:-\:5\:-\:2}$

$\displaystyle{\implies\sf\:x\:\leq\:3\:\quad\:OR\:\quad\:x\:\geq\:-\:7}$

$\displaystyle{\therefore\:\boxed{\blue{\sf\:-\:7\:\leq\:x\:\leq\:3\:}}}$

$\displaystyle{\implies\:\underline{\boxed{\red{\sf\:x\:\leq\:3}}}\sf\:\quad\:OR\:\quad\:\underline{\boxed{\red{\sf\:x\:\geq\:-\:7\:}}}}$

The solution set for the given equation

$\displaystyle{\boxed{\pink{\sf\:x\:\in\:\{\:-\:7,\:-\:6,\:-\:5,\:-\:4,\:-\:3,\:-\:2,\:-\:1,\:0,\:1,\:2,\:3\:\}\:}}}$