To solve the inequality 2 ( 4 + 2 x ) ≥ 5 x + 5 {\displaystyle 2(4+2x)\geq 5x+5} , you need to follow these steps:
Expand the brackets on the left side of the inequality by multiplying 2 with each term inside: 8 + 4 x ≥ 5 x + 5 {\displaystyle 8+4x\geq 5x+5}
Subtract 4 x {\displaystyle 4x} from both sides of the inequality to get all the x terms on one side: 8 ≥ x + 5 {\displaystyle 8\geq x+5}
Subtract 5 from both sides of the inequality to get all the constants on one side: 3 ≥ x {\displaystyle 3\geq x}
Switch the sides of the inequality and reverse the sign to get the variable on the left side: x ≤ 3 {\displaystyle x\leq 3}
The solution is x ≤ 3. This means that any value of x that is less than or equal to 3 will make the inequality true. You can check your answer by plugging in some values of x into the original inequality and see if it holds. For example, if x = -2, then:
2 ( 4 + 2 ( − 2 ) ) ≥ 5 ( − 2 ) + 5 {\displaystyle 2(4+2(-2))\geq 5(-2)+5} 2 ( 4 − 4 ) ≥ − 10 + 5 {\displaystyle 2(4-4)\geq -10+5} 0 ≥ − 5 {\displaystyle 0\geq -5}
This is a true statement, so x = -2 is a valid solution. You can also graph the solution on a number line or a coordinate plane. Here is a video that explains how to do that.