Question

multiply both sides: multiply both sides by what?
1.4(□) = 2.5x(□)

Explanation:

Step1: Identify the goal

We want to eliminate the coefficient of \(x\) or simplify the equation. To solve for \(x\) in an equation like \(1.4 = 2.5x\) (assuming the original equation was \(1.4=2.5x\)), we multiply both sides by the reciprocal of \(2.5\) or a number to clear decimals. But if we want to eliminate the decimal, we can multiply both sides by 10 (since both 1.4 and 2.5 have one decimal place, multiplying by 10 will make them integers). Wait, maybe the original equation is \(1.4=2.5x\), and we need to multiply both sides by the same number. Let's assume we want to solve for \(x\), so we multiply both sides by \(\frac{1}{2.5}\) or 10 to eliminate decimals. Let's check: if we multiply both sides by 10, we get \(1.4\times10 = 2.5x\times10\), which is \(14 = 25x\). But maybe the problem is to multiply both sides by the same number to solve for \(x\). Let's see the blanks: \(1.4(\square)=2.5x(\square)\). So we need to put the same number in both blanks. To isolate \(x\), we can multiply both sides by \(\frac{1}{2.5}\) or \(\frac{10}{25}=\frac{2}{5}\), but maybe the intended number is 10 to eliminate decimals. Wait, let's think again. If the equation is \(1.4 = 2.5x\), then to solve for \(x\), we divide both sides by 2.5, which is the same as multiplying both sides by \(\frac{1}{2.5}\) or 0.4. But 2.5 times 0.4 is 1. Let's check: \(2.5\times0.4 = 1\), so if we multiply both sides by 0.4, we get \(1.4\times0.4=2.5x\times0.4\), so \(0.56 = x\). But maybe the problem is to multiply both sides by 10 to eliminate decimals. Let's see: \(1.4\times10 = 14\), \(2.5x\times10 = 25x\). So the number to multiply both sides is 10. So we put 10 in both blanks.

Step2: Fill in the blanks

We need to multiply both sides by the same number. Let's choose 10 (to eliminate decimals). So:
\(1.4\times10 = 2.5x\times10\)

Answer:

The number to multiply both sides is 10, so the blanks are filled with 10 and 10. So \(1.4(\boldsymbol{10}) = 2.5x(\boldsymbol{10})\)