Question

Solve and graph the inequality. −x4−6≥−8 {"version":"1.1","math":"-x4-6≥-8"} Question 6 options: x ≤ 8 x < –4 x > 8 x ≥ –8 Save Question 7 (5 points) Question 7 Unsaved Solve and graph the inequality. 6.7 ≥−0.2x + 4.5 {"version":"1.1","math":"6.7 ≥-0.2x + 4.5"} Question 7 options: x≥−11 {"version":"1.1","math":"x≥-11"} x≥−56 {"version":"1.1","math":"x≥-56"} x<−11 {"version":"1.1","math":"x<-11"} x < −56 {"version":"1.1","math":"x < -56"}

Answer 1

Question 6: Option 1.

Question 7: Option 1.

Explanation:

Question 6: The given inequality is

`-(x)/(4)-6\geq -8`

Add 6 on both sides.

`-(x)/(4)-6+6\geq -8+6`

`-(x)/(4)\geq -2`

Multiply both sides by -4. If we multiply or divide an inequality by a negative number, then we need to change the sign of inequality.

`-(x)/(4)* (-4)\leq -2* (-4)`

`x\leq 8`

Therefore, the correct option is 1.

Question 7: The given inequality is

`6.7\geq -0.2x+4.5`

Subtract 4.5 from both sides.

`6.7-4.5\geq -0.2x+4.5-4.5`

`2.2\geq -0.2x`

Divide both sides by 2.2.

`-11\leq x`

It can be rewritten as

`x\geq -11`

Therefore, the correct option is 1.

Answer 2

1. Answer: x < –4
The question is a bit ambiguous since x4 can be interpreted as x^4. Since there was no option for −x^4−6 ≥ −8 , I will solve the question assuming that the original question was −x(4−6)≥−8
−x(4−6)≥−8 −x(-2)≥−8 ---> multiply x with -2 2x≥−8 ----> divide by 2x≥−4
2. Answer: x≥ -11
To solve inequality using > or < sign, you must be careful because multiplying the inequality with -1 will cause the sign to change direction(< will become > or vice versa). In this case, will solve the question without multiplying it with -1

6.7 ≥−0.2x + 4.5 ----> move -0.2x to left, 6.7 to right
0.2x ≥ 4.5 - 6.7
0.2x ≥ -2.2
x≥ -11