Question

1. 7x+30=19x-62. 0.6(x-6)+14.2=0.8(8-x)3. (-2x-5)(0.3x+2.7)=0​

Answer 1

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Answer 2

Let's solve each equation step by step:

1. 7x + 30 = 19x - 62:

To isolate the variable x, we can start by moving the terms with x to one side of the equation and the constant terms to the other side:

7x - 19x = -62 - 30

Simplifying:

-12x = -92

Next, divide both sides of the equation by -12 to solve for x:

x = (-92) / (-12)

Simplifying further:

x = 23/3

So the solution to the equation is x = 23/3 or approximately 7.67.

2. 0.6(x - 6) + 14.2 = 0.8(8 - x):

First, let's distribute the 0.6 and 0.8 terms:

0.6x - 3.6 + 14.2 = 6.4 - 0.8x

Combining like terms:

0.6x + 10.6 = 6.4 - 0.8x

Now, let's move the terms with x to one side and the constant terms to the other side:

0.6x + 0.8x = 6.4 - 10.6

Simplifying:

1.4x = -4.2

Dividing both sides by 1.4:

x = -4.2 / 1.4

Simplifying further:

x = -3

Therefore, the solution to the equation is x = -3.

3. (-2x - 5)(0.3x + 2.7) = 0:

To solve this equation, we'll use the zero product property. This property states that if the product of two factors is zero, then at least one of the factors must be zero.

So we set each factor equal to zero:

-2x - 5 = 0 or 0.3x + 2.7 = 0

Solving the first equation:

-2x = 5 x = 5 / -2 x = -2.5

Solving the second equation:

0.3x = -2.7 x = -2.7 / 0.3 x = -9

Therefore, the solutions to the equation are x = -2.5 and x = -9.