Introduction to Compound Inequalities — Unit test Answers

If Dominik completes a project by himself, it will take him 8 hours. Working with Katarina, it will take them 5 hours. If they work together, what is the missing value from the table that represents the part of the project Dominik will complete?

How many solutions exist for the given equation?3(x + 10) + 6 = 3(x + 12)

Four milliliters of ink A is added to 10 milliliters of ink B, forming a mixture of inks. Ink A contains 10% blue pigment. Ink B contains an unknown percentage of blue pigment. The mixture of the two inks contains 35% blue pigment.What percentage of blue pigment is in ink B?

Last week, Lindsay earned $10 per hour plus a $60 bonus for good job performance. She spends of her paycheck on dinner with friends. If she had not earned the bonus, the amount she spent on dinner would have been of her paycheck. Which equation can be used to find h, the number of hours Lindsay worked last week?

What value of x is in the solution set of the inequality –2(3x + 2) > –8x + 6?

What is the solution to –4(8 – 3x) ≥ 6x – 8?

Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?

The solution is n = –2 verified as a solution to the equation 1.4n + 2 = 2n + 3.2. What is the last line of the justification?

Bianca wrote the steps for her solution to the equation 2.3 + 8(1.3x – 4.75) = 629.9. She left out the description for the last step.What is the missing step of her solution?

Solve the equation.–x + 8 + 3x = x – 6

Laurie is trying to stay within 10 feet of her current diving depth of –30 feet (with regard to sea level) so that the light is still good but she can be close to the sea life during her scuba dive. Which two equations can be used to find the minimum and maximum depths Laurie wants to stay between?

What is the solution to 3|–3x + 9| = –18?

The amount of potential energy, P, an object has is equal to the product of its mass, m, its height off the ground, h, and the gravitational constant, g. This can be modeled by the equation P = mgh.

To fit in an existing frame, the length, x, of a piece of glass must be longer than 12 cm but not longer than 12.2 cm. Which inequality can be used to represent the lengths of the glass that will fit in the frame?

Which compound inequality is represented by the graph?

Solve the inequality.2(4+2x)≥5x+5

What interval includes all possible values of x, where –3(6 – 2x) ≥ 4x + 12?

Working together, Melissa and Jing can mow a lawn in 5 hours. It would take Melissa 8 hours to do the job alone.

Which number line represents the solution set for the inequality 3x < –9?