Question

What is the value of x in the equation 1.5(x + 4) – 3 = 4.5(x – 2)? 3 4 5 9

Answer 1

1.5(x+4)-3=4.5(x-2)

First, distribute 1.5 into x and 4, and 4.5 into x and -2, to get rid of the parentheses. Everything that we do to solve this equation is to isolate x to solve for its value.

1.5x+6-3=4.5x-9

Combine like terms on both sides (6-3).

1.5x+3=4.5x-9

Subtract 1.5x from both sides.

3=3x-9

Add 9 to both sides.

12=3x

Divide both sides by 3.

4=x

The answer is 4.

I hope this helps :)

Answer 2

The value of 'x' in the considered equation is evaluated as shown by: Option B: 4

How can we find the solution to an equation?

We do same operations on both the sides so that equality of both expressions doesn't get disturbed. Solving equations generally means finding the values of the variables used in it for which the considered equation is true.

Sometimes we can find such value, and sometimes it is not possible at all, or sometimes, there are infinite number of solutions.

What is distributive property of multiplication over addition?

Suppose a, b and c are three numbers. Then we have:

$a(b + c) = a\times b + a\times c$

(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)

Sign multiply

$(-ve \times (+ve) = -ve\\(-ve) \times (-ve) = +ve\\(+ve) \times (+ve) = +ve\\(+ve) \times (-ve) = -ve$

where -ve, +ve are sign of operands and result.

For this case, the considered algebraic equation is

$1.5(x + 4) - 3 = 4.5(x - 2)$

Using the distributive property of multiplication over addition, we get:

$1.5(x + 4) - 3 = 4.5(x - 2)\\1.5x + 6 - 3 = 4.5x -9\\1.5x + 3 = 4.5x - 9\\\\\text{Adding 9 - 1.5x on both the sides}\\1.5x + 3 + 9 - 1.5x = 4.5x - 9 + 9 - 1.5x\\12 = (4.5 - 1.5)x\\12 = 3x\\\\\text{Dividing both the sides by 3}\\4 = x\\x = 4$

Thus, the value of the variable x comes out to be 4. This is the solution of the equation as for this value of x(and only for this value), the equation will be true, else false. (you can put 4 in place of x and see that both left and right side of the equation will come equal to each other. They won't do so for any other value).

Thus, the value of 'x' in the considered equation is evaluated as shown by: Option B: 4

Learn more about solution of equations here:

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