3x - 1 < x + 5, x = 1
Sub in our x = 1 value
3(1) - 1 < (1) + 5
3 - 1 < 1 + 5
2 < 6,
2 is less than 6, so the statement is true when x = 1
4(x + 2) > {3x + 4} / 2, x = - 4
Sub in x = -4,
4((-4) + 2) > (3(-4) + 4) / 2
Doing the brackets first,
4((-4) + 2) > ((-12) + 4) / 2
4(-2) > (-8) / 2
-8 > -4,
Remembering our number line, -8 is less than -4,
Therefore, the statement is false for x = -4
x2 - 6x + 2 ≥ 12 + 3x, x = 2
Sub in x = 2
(2) 2 - 6(2) + 2 ≥ 12 + 3(2)
Exponents first,
4 - 6(2) + 2 ≥ 12 + 3(2)
Multiply,
4 - 12 + 2 ≥ 12 + 6
-6 ≥ 18,
We know, that 18 is greater than -6, so,
The statement is false for x = -4
{x - 3} / 6 ≤ {-3(x + 2)} / 7, x = -9,
Sub in x = - 9
((-9) - 3) / 6 ≤ (-3((-9) + 2)) / 7
Brackets first,
((-9) - 3) / 6 ≤ (-3(-7)) / 7
(-12) / 6 ≤ (21) / 7
-2 ≤ 3,
We know that 3 is greater than -2, so it fits the statement “-2 ≤ 3”,
Therefore, the statement is true for x = -9