solve the compound inequality.
9 – 4x ≥ 5 or 4(–1 + x) – 6 ≥ 2

a. x ≥ 1 or x ≥ 3
b. x ≤ 1 or x ≥ 3
c. x ≤ –1 or x ≤ 3
d. x ≥ –1 or x ≥ 3

The compound inequality for 9 – 4x ≥ 5 or 4(–1 + x) – 6 ≥ 2 is:

Option A is correct.

A compound inequality is one that is formed by combining two simple inequalities. They are derived form of fundamental inequalities.

From the question:

The first thing to do is to open the brackets and move the like terms to the same sides.

So,

9 - 5  ≥  4x    or    -4  + 4x - 6   ≥  2

4   ≥ 4x         or      -10 + 4x   ≥  2

4   ≥ 4x         or       4x   ≥ 10 + 2

4   ≥ 4x         or       4x  ≥  12

4x  ≥ 4         or        4x  ≥  12

Divide both sides by 4

x  ≥ 1     or     x  ≥  3

Therefore, the compound inequality of 9 – 4x ≥ 5 or 4(–1 + x) – 6 ≥ 2 is:

x  ≥ 1     or     x  ≥  3

Learn more about compound inequality here:

link

Step-by-step explanation:

9 - 4x > = 5                         or               4(-1 + x) - 6 > = 2

-4x > = 5 - 9                                           -4 + 4x - 6 > = 2

-4x > = -4                                                4x - 10 > = 2

x < = -4/-4                                              4x > = 2 + 10  

x < = 1                                                    4x > = 12

                                                              x > = 12/4

                                                              x > = 3

answer is : B

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c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.