solve the inequality and write the solution set using interval notation.
4x+7 <2x+5
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-3
To solve the inequality 4x + 7 < 2x + 5, we need to isolate the variable x. Here's how to do it:
1. Start by subtracting 2x from both sides of the inequality to eliminate the x term on the right side:
4x + 7 - 2x < 2x + 5 - 2x
Simplifying, we get:
2x + 7 < 5
2. Next, subtract 7 from both sides of the inequality to isolate the 2x term:
2x + 7 - 7 < 5 - 7
Simplifying, we get:
2x < -2
3. Finally, divide both sides of the inequality by 2 to solve for x:
(2x)/2 < (-2)/2
Simplifying, we get:
x < -1
Therefore, the solution to the inequality is x < -1.
To represent this solution in interval notation, we write:
(-∞, -1)