7x+39≥53 AND16x+15>31
7x+39≥53 AND16x+15>31
7x ≥ 14 AND 16x > 16
x ≥ 2 AND x > 1
x ≥ 2 , show on a number line to illustrate
To simplify and solve the inequalities step-by-step:
1. 7x + 39 ≥ 53:
Subtract 39 from both sides:
7x ≥ 53 - 39
7x ≥ 14
2. Divide both sides by 7 to isolate x:
x ≥ 14 / 7
x ≥ 2
So, the solution for this inequality is x ≥ 2.
3. 16x + 15 > 31:
Subtract 15 from both sides:
16x > 31 - 15
16x > 16
4. Divide both sides by 16 to isolate x:
x > 16 / 16
x > 1
So, the solution for this inequality is x > 1.
In summary:
- For the inequality 7x + 39 ≥ 53, the solution is x ≥ 2.
- For the inequality 16x + 15 > 31, the solution is x > 1.
To solve the inequality 7x + 39 ≥ 53, you can follow these steps:
Step 1: Subtract 39 from both sides of the inequality to isolate the term with x:
7x + 39 - 39 ≥ 53 - 39
7x ≥ 14
Step 2: Divide both sides of the inequality by 7 to solve for x:
7x/7 ≥ 14/7
x ≥ 2
Therefore, the solution to the inequality 7x + 39 ≥ 53 is x ≥ 2.
Now, let's move on to the next inequality: 16x + 15 > 31.
To solve this inequality, follow these steps:
Step 1: Subtract 15 from both sides of the inequality to isolate the term with x:
16x + 15 - 15 > 31 - 15
16x > 16
Step 2: Divide both sides of the inequality by 16 to solve for x:
16x/16 > 16/16
x > 1
Therefore, the solution to the inequality 16x + 15 > 31 is x > 1.
In summary, the solutions to the two inequalities are:
For 7x + 39 ≥ 53, x ≥ 2.
For 16x + 15 > 31, x > 1.