Question

solve this equation. 24 + 0.44x = 19 + 1.69x x = 4 x = 0.44 x = 5 x = 5.4

Explanation:

Step1: Subtract \(0.44x\) from both sides

To get all the \(x\)-terms on one side, we subtract \(0.44x\) from both sides of the equation \(24 + 0.44x = 19 + 1.69x\). This gives us \(24 = 19 + 1.69x - 0.44x\). Simplifying the right side, we have \(24 = 19 + 1.25x\).

Step2: Subtract 19 from both sides

Next, we subtract 19 from both sides to isolate the term with \(x\). So, \(24 - 19 = 1.25x\), which simplifies to \(5 = 1.25x\).

Step3: Divide both sides by 1.25

To solve for \(x\), we divide both sides of the equation \(5 = 1.25x\) by 1.25. This gives us \(x=\frac{5}{1.25}\), and calculating that, we get \(x = 4\). Wait, no, wait. Wait, \(5\div1.25 = 4\)? Wait, no, \(1.25\times4 = 5\), yes. Wait, but let's check again. Wait, step 1: \(24 + 0.44x - 0.44x = 19 + 1.69x - 0.44x\) gives \(24 = 19 + 1.25x\). Then step 2: \(24 - 19 = 1.25x\) gives \(5 = 1.25x\). Then step 3: \(x=\frac{5}{1.25}=4\)? Wait, but let's check the answer. Wait, maybe I made a mistake. Wait, \(1.69 - 0.44 = 1.25\), correct. Then \(24 - 19 = 5\), correct. Then \(5\div1.25 = 4\), so \(x = 4\). But let's check the options. One of the options is \(x = 4\), so that's the answer. Wait, but let's verify by plugging \(x = 4\) back into the original equation. Left side: \(24 + 0.44\times4 = 24 + 1.76 = 25.76\). Right side: \(19 + 1.69\times4 = 19 + 6.76 = 25.76\). So it works. Wait, but wait, maybe I miscalculated earlier. Wait, no, the steps are correct. So the answer is \(x = 4\). Wait, but let's check the options again. The options are \(x = 4\), \(x = 0.44\), \(x = 5\), \(x = 5.4\). So the correct one is \(x = 4\). Wait, but wait, when I did \(5\div1.25\), that's 4? Wait, 1.25 times 4 is 5, yes. So that's correct.

Wait, but let's check the original equation again. \(24 + 0.44x = 19 + 1.69x\). Let's plug \(x = 4\): left side is \(24 + 0.44*4 = 24 + 1.76 = 25.76\). Right side is \(19 + 1.69*4 = 19 + 6.76 = 25.76\). So they are equal. So \(x = 4\) is correct.

Answer:

\(x = 4\) (corresponding to the option "x = 4")