Which of the following is a solution of the inequality
-3 is less than 2x +1 is less than 5
Answer = 4
Nope. Inequalities do not have a single value for a solution.
-3 < 2x+1 < 5
-4 < 2x < 4
-2 < x < 2
Clearly 4 does not work.
2*4+1 is not less than 5.
Any value between -2 and 2 will work.
Ok thank you
To find the solution to the given inequality, we will follow these steps:
Step 1: Solve each inequality separately:
i. -3 < 2x + 1
ii. 2x + 1 < 5
Step 2: Solve the first inequality:
-3 < 2x + 1
Subtract 1 from both sides:
-3 - 1 < 2x + 1 - 1
-4 < 2x
Divide both sides by 2:
-4/2 < 2x/2
-2 < x
So, the solution to the first inequality is x > -2.
Step 3: Solve the second inequality:
2x + 1 < 5
Subtract 1 from both sides:
2x + 1 - 1 < 5 - 1
2x < 4
Divide both sides by 2:
2x/2 < 4/2
x < 2
So, the solution to the second inequality is x < 2.
Step 4: Combine the solutions:
Combining the solutions from both inequalities, we get:
-2 < x < 2
So, any value of x within the range -2 to 2 (excluding -2 and 2) will be a solution to the given inequality.
Therefore, the answer 4 is not a solution.