193k views
2 votes
Solve the inequality.

2(4+2x)≥5x+5

x≤−2
x≥−2
x≤3
x≥3

User Mathfux
by
8.9k points

2 Answers

1 vote

Answer:

x ≤ -2.

Explanation:

Let's solve the inequality step-by-step:

2(4 + 2x) ≥ 5x + 5

First, distribute the 2 on the left side of the inequality:

8 + 4x ≥ 5x + 5

Next, move the variables to one side and constants to the other side of the inequality:

8 - 5 ≥ 5x - 4x + 5

3 ≥ x + 5

Now, isolate the variable by subtracting 5 from both sides:

3 - 5 ≥ x

-2 ≥ x

So, the solution to the inequality is x ≤ -2.
User Tanoro
by
9.1k points
2 votes

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.

User GLK
by
7.7k points

Related questions

2 answers
2 votes
66.3k views
2 answers
2 votes
42.7k views
1 answer
3 votes
128k views