The following inequality is solved for x.
Which Line shows the inequality after you combine like terms?
Line A 4(x + 1) + 8 ≥ 4 + 2x
Line B 4x + 4 + 8 ≥ 4 + 2x
Line C 4x + 12 ≥ 4 + 2x
Line D 2x + 12 ≥ 4
Line E 2x ≥ - 8
Line F x ≥ -4
Which Line shows the inequality after you combine like terms?
Line C 4x + 12 ≥ 4 + 2x
The Line that shows the inequality after combining like terms is Line C: 4x + 12 ≥ 4 + 2x.
To combine like terms in an inequality, you need to simplify the expression by adding or subtracting similar terms.
Let's analyze the options given:
Line A: 4(x + 1) + 8 ≥ 4 + 2x
In this line, you can simplify by using the distributive property: 4 * x = 4x, and 4 * 1 = 4.
Result: 4x + 4 + 8 ≥ 4 + 2x
Line B: 4x + 4 + 8 ≥ 4 + 2x
There are no like terms to combine in this line.
Line C: 4x + 12 ≥ 4 + 2x
Here, you can combine the x terms by subtracting 2x from both sides:
Result: 4x - 2x + 12 ≥ 4
Line D: 2x + 12 ≥ 4
There are no like terms to combine in this line.
Line E: 2x ≥ -8
There are no like terms to combine in this line.
Line F: x ≥ -4
There are no like terms to combine in this line.
From the analysis above, the line that shows the inequality after combining like terms is:
Line C: 4x + 12 ≥ 4 + 2x