Identify the inequality with x = 3 as a solution. Select all that apply.
x + 3 < 4(x + 1) + 2
2x - 8 ≥ 7 - 3x
3(x + 2) < 14 - x
4(x - 1) < x + 5
5 - 2( x + 1) > x
6(x - 4) ≤ 2x
To find the inequality with x = 3 as a solution, substitute 3 for x in each inequality and see if the resulting statement is true.
x + 3 < 4(x + 1) + 2
3 + 3 < 4(3 + 1) + 2
6 < 4(4) + 2
6 < 16 + 2
6 < 18
This inequality is true when x = 3.
2x - 8 ≥ 7 - 3x
2(3) - 8 ≥ 7 - 3(3)
6 - 8 ≥ 7 - 9
-2 ≥ -2
This inequality is true when x = 3.
3(x + 2) < 14 - x
3(3 + 2) < 14 - 3
15 < 14 - 3
15 < 11
This inequality is false when x = 3.
4(x - 1) < x + 5
4(3 - 1) < 3 + 5
8 < 8
This inequality is false when x = 3.
5 - 2( x + 1) > x
5 - 2(3 + 1) > 3
5 - 2(4) > 3
5 - 8 > 3
-3 > 3
This inequality is false when x = 3.
6(x - 4) ≤ 2x
6(3 - 4) ≤ 2(3)
6(-1) ≤ 6
-6 ≤ 6
This inequality is true when x = 3.
Therefore, the inequalities with x = 3 as a solution are:
x + 3 < 4(x + 1) + 2
2x - 8 ≥ 7 - 3x
6(x - 4) ≤ 2x
The following inequality is solved for x.
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 B
Line C
Line D
Line E
Line F
The Line that shows the inequality after combining like terms is Line C: 4x + 12 ≥ 4 + 2x.
Mari is solving the inequality 4(x - 3) > 16. Her first step is 4x - 12 > 16.
Which step could be the next step? Select all that apply.
4x - 12 + 12 > 16 + 12
4x - 12 - (-12) > 16 - (-12)
(14)(4x − 12) > 16 (1(4))
4x4 − 12 > 164
4(4x - 12) > 16(4)
The next step could be:
4x - 12 + 12 > 16 + 12
This step involves adding 12 to both sides of the inequality.
Mari is solving the inequality 4(x - 3) > 16. Her first step is 4x - 12 > 16.
Which step could be the next step? Select all that apply.
4x - 12 + 12 > 16 + 12
4x - 12 - (-12) > 16 - (-12)
(1/4)(4x-12)>16(1/(4))
4x/4-12>16/4
4(4x - 12) > 16(4)
The next steps could be:
4x - 12 + 12 > 16 + 12
This step involves adding 12 to both sides of the inequality.
4x - 12 - (-12) > 16 - (-12)
This step involves subtracting -12 (which is the same as adding 12) to both sides of the inequality.
4(4x - 12) > 16(4)
This step involves multiplying both sides of the inequality by 4.
Javon and Ivy are both given the equation 5-2x-1/3≤4 Javon thinks the first step is -2x-1/3≤9 Ivy thinks the first step is -2x-1/3≤-1 Who is incorrect and why?
Ivy is incorrect because, on her first step, she did not add 5 (or equivalently subtract -5) from both sides of the equation.
Both students are incorrect because, on their first step, they did not multiply by 3 on both sides of the equation.
Both students are incorrect because, on their first step, they did not divide by 3 (or equivalently multiply by 1/3) from both sides of the equation.
Javon is incorrect because, on his first step, he did not subtract 5 ( or equivalently add -5) from both sides of the equation.
Both students are incorrect because, on their first step, they did not add 5 (or equivalently subtract -5) from both sides of the equation.
Javon and Ivy are both given the equation 5-2x-1/3≤4 Javon thinks the first step is -2x-1/3≤9 Ivy thinks the first step is -2x-1/3≤-1 Who is incorrect and why?
Ivy is incorrect because, on her first step, she did not add 5 (or equivalently subtract -5) from both sides of the equation.
Both students are incorrect because, on their first step, they did not multiply by 3 on both sides of the equation.
Both students are incorrect because, on their first step, they did not divide by 3 (or equivalently multiply by 1/3) from both sides of the equation.
Javon is incorrect because, on his first step, he did not subtract 5 ( or equivalently add -5) from both sides of the equation.
Consider the inequality 3( - 1 - x) ≤ -2x - 3x