Equations / Inequalities

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SAT Math › Equations / Inequalities

Questions 1 - 10

Solve for :

$x\leq11$

Explanation

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.

Subtract on both sides.

Divide on both sides.

Three consecutive even numbers add to 42. What is the middle number?

$14$

$10$

$12$

$16$

$18$

Explanation

Let $x$ = 1st even number, $x+2$ = 2nd even number, and $x+4$ = 3rd even number.

Then the equation to solve becomes $x+(x+2)+(x+4)=42$ .

$3x+6=42$

Thus $x=12,x+2=14,\ and\ x+4=16$ , so the middle number is 14.

Translate into an algebraic expression:

One third of the difference of a number and 3 equals five times the number.

$\frac{1}{3}\left ( x-3 \right )=5x$

$\frac{1}{3}x-3=5$

$\frac{1}{3}x-3=5x$

$\frac{1}{3}\left ( x+3 \right )= 5x$

$3\left ( x-3 \right )=5x$

Explanation

You have to form the difference first and must be enclosed in parentheses which gets multiplied by 1/3. The word "equals" means the "=" symbol

Pets Plus makes bird houses. Their monthly fixed expenses are $750. The cost for each bird house is $15. The bird houses sell for $40.

If Pets Plus sells 50 bird houses, what is the profit?

$\$500$

$\$250$

$\$750$

$\$300$

$\$625$

Explanation

Let $x$ = the number of birdhouses sold each month.

$Revenue=40x$

$Costs=15x+750$

$Profit = Revenue-Costs$

$=40x-15x-750$

$=25x-750$

Substituting in 50 for $x$ gives an answer of 500, so the profit on 50 birdhouses is $500.

Solve _x_2 – 48 = 0.

x = 4 or x = –4

x = 4√3

x = 4√3 or x = –4√3

x = –√48

x = 0

Explanation

No common terms cancel out, and this isn't a difference of squares.

Let's move the 48 to the other side: _x_2 = 48

Now take the square root of both sides: x = √48 or x = –√48. Don't forget the second (negative) solution!

Now √48 = √(3*16) = √(3*42) = 4√3, so the answer is x = 4√3 or x = –4√3.

The sum of four consecutive even integers is , but their product is . What is the least of those integers?

Explanation

Any time the product of consecutive numbers is , must be a one of those consecutive numbers, because if it is not, the product will be non-zero. This leaves us with four possibilities, depending on where is placed in the sequence.

As we can see, , , and are our numbers in question, meaning is our answer as the lowest number.

Note that it is possible to use algebra and set up a system of equations, but it's more time-consuming, which could hinder more than help in a standardized test setting.

Two cars start 25 mile apart and drive away from each other in opposite directions at speeds of 50 and 70 miles per hour. In approximately how many minutes will they be 400 miles apart?

None of the other answers

187.5

200

3.33

3.125

Explanation

The cars have a distance from each other of 25 + 120t miles, where t is the number of hours, 25 is their initial distance and 120 is 50 + 70, or their combined speeds. Solve this equation for 400:

25 + 120t = 400; 120t = 375; t = 3.125

However, the question asked for minutes, so we must multiply this by 60:

3.125 * 60 = 187.5 minutes.

If 5 + x is 5 more than 5,what is the value of 2_x_?

Explanation

5 more than 5 = 10

5 + x = 10

Subtract 5 from each side of the equation: x = 5 → 2_x_ = 10

The sum of four consecutive even integers is , but their product is . What is the least of those integers?

Explanation

As we can see, , , and are our numbers in question, meaning is our answer as the lowest number.

Note that it is possible to use algebra and set up a system of equations, but it's more time-consuming, which could hinder more than help in a standardized test setting.

If 7_x_ + y = 25 and 6_x_ + y = 23, what is the value of x?