Question

Multiply the equation by a power of 10 to write an equivalent equation with integer coefficients. $$ 2.5 x+0.7=4.6-1.3 x $$

Short answer

The equivalent equation with integer coefficients is \(25x + 7 = 46 - 13x\)

Step-by-step solution

Title: Identify the Decimals

Firstly, look at the equation \(2.5x + 0.7 = 4.6 - 1.3x\). Identify the decimal places in the coefficients.

Title: Determine the power of 10

Next, determine the power of 10 that will eliminate all decimals. Here, the highest number of decimal places is 1. Therefore, multiplying the entire equation by \(10^1 = 10\) will convert the equation to integer coefficients.

Title: Multiply the equation

Now, multiply every term in the equation by 10. So the equation becomes: \(10 * 2.5x + 10 * 0.7 = 10 * 4.6 - 10 * 1.3x\), which simplifies to \(25x + 7 = 46 - 13x\)