Ten less than twice a number is equal to at most 52. What are all the possible values of the number? Inuk wrote the inequality 2x−10≤52 , where x equals the number, to help solve this problem. Solve his inequality. Use the letter x as your variable and write your x term first.
The inequality 2x - 10 ≤ 52 can be solved as follows:
Adding 10 to both sides of the inequality, we get:
2x - 10 + 10 ≤ 52 + 10
2x ≤ 62
Dividing both sides of the inequality by 2, we get:
(2x)/2 ≤ 62/2
x ≤ 31
Therefore, the possible values of the number, x, are all real numbers less than or equal to 31.
To solve the inequality 2x - 10 ≤ 52, we need to isolate the variable x. Let's go step by step:
1. Start with the given inequality: 2x - 10 ≤ 52.
2. First, add 10 to both sides of the inequality to get rid of the -10:
2x - 10 + 10 ≤ 52 + 10.
Simplifying, we have: 2x ≤ 62.
3. Next, divide both sides of the inequality by 2 to isolate x:
(2x) / 2 ≤ 62 / 2.
Simplifying, we have: x ≤ 31.
So, the solution to the inequality 2x - 10 ≤ 52 is x ≤ 31. This means that the number x can be any value less than or equal to 31 in order to satisfy the given inequality.
Helena will receive $53 plus $4 per kid for babysitting this afternoon. She is hoping to make at least $69. How many kids does she need to babysit? She writes the inequality 4x+53≥69 , where x equals the number of kids, to help figure this out. Solve her inequality. Use the letter x as your variable and write your x term first.
The inequality 4x + 53 ≥ 69 can be solved as follows:
Subtracting 53 from both sides of the inequality, we get:
4x + 53 - 53 ≥ 69 - 53
4x ≥ 16
Dividing both sides of the inequality by 4, we get:
(4x)/4 ≥ 16/4
x ≥ 4
Therefore, Helena needs to babysit at least 4 kids in order to make at least $69.