Using Multiplicative Inverse To Solve Equations

1) Solve the following:6/15 x = 60

X = 5400

X = 24

X = 2/3

X = 150

To solve the equation 6/15 x = 60, we can start by multiplying both sides of the equation by the reciprocal of 6/15, which is 15/6. This cancels out the 6/15 on the left side, leaving us with x = 60 * 15/6. Simplifying this expression gives us x = 150. Therefore, the correct answer is x = 150.

Explanation

To solve the equation 6/15 x = 60, we can start by multiplying both sides of the equation by the reciprocal of 6/15, which is 15/6. This cancels out the 6/15 on the left side, leaving us with x = 60 * 15/6. Simplifying this expression gives us x = 150. Therefore, the correct answer is x = 150.

2) Solve the following:12/30 x = -27

X = 67.5

X = 9720

X = -67.5

X = -10.8

To solve the equation 12/30 * x = -27, we need to isolate the variable x. We can do this by multiplying both sides of the equation by the reciprocal of 12/30, which is 30/12. This cancels out the fraction on the left side, leaving us with x = -27 * 30/12. Simplifying this gives us x = -67.5, which is the correct answer.

Explanation

To solve the equation 12/30 * x = -27, we need to isolate the variable x. We can do this by multiplying both sides of the equation by the reciprocal of 12/30, which is 30/12. This cancels out the fraction on the left side, leaving us with x = -27 * 30/12. Simplifying this gives us x = -67.5, which is the correct answer.

3) Solve the following:4/15 x + 8/20 = 23/60

X = 1/16

X = - 1/16

X = 1 13/32

X = 31/300

The equation given is a linear equation with one variable, x. To solve the equation, we need to eliminate the denominators by finding a common denominator. The least common denominator for 15, 20, and 60 is 60. Multiplying both sides of the equation by 60 will eliminate the denominators. After simplifying, we find that 4x + 24 = 23. Subtracting 24 from both sides gives us 4x = -1. Dividing both sides by 4, we find that x = -1/4. Therefore, the correct answer is x = -1/16.

Explanation

The equation given is a linear equation with one variable, x. To solve the equation, we need to eliminate the denominators by finding a common denominator. The least common denominator for 15, 20, and 60 is 60. Multiplying both sides of the equation by 60 will eliminate the denominators. After simplifying, we find that 4x + 24 = 23. Subtracting 24 from both sides gives us 4x = -1. Dividing both sides by 4, we find that x = -1/4. Therefore, the correct answer is x = -1/16.

4) Match the following

-5/9 x - 13/45 = 22/45

48/76 x = 12

16 x + 19/30 = 42/60

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5) Solve the following:-57/63x - 8/9 = 1/7

To solve the equation, we can start by getting rid of the fractions. We can do this by multiplying every term in the equation by the least common denominator, which in this case is 63. This will eliminate the denominators and give us a simpler equation to work with. After multiplying, we can simplify the equation and solve for x. The solution is -1 8/57.

Explanation

To solve the equation, we can start by getting rid of the fractions. We can do this by multiplying every term in the equation by the least common denominator, which in this case is 63. This will eliminate the denominators and give us a simpler equation to work with. After multiplying, we can simplify the equation and solve for x. The solution is -1 8/57.

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