Question

6.
11(4 - 2x) = -4(4x + 4) - 2x

x = 15 \t x = -15 \t x = 1.5
yellow \t red \t blue

Explanation:

Step1: Expand both sides

Expand \(11(4 - 2x)\) to get \(44 - 22x\). Expand \(-4(4x + 4)-2x\): first, \(-4(4x + 4)=-16x - 16\), then add \(-2x\) to get \(-16x - 16 - 2x=-18x - 16\). So the equation becomes \(44 - 22x=-18x - 16\).

Step2: Move terms with x to one side

Add \(22x\) to both sides: \(44=-18x - 16 + 22x\), which simplifies to \(44 = 4x - 16\).

Step3: Solve for x

Add 16 to both sides: \(44 + 16 = 4x\), so \(60 = 4x\). Divide both sides by 4: \(x=\frac{60}{4}=15\). Wait, but let's check again. Wait, maybe I made a mistake. Wait, original equation: \(11(4 - 2x)=-4(4x + 4)-2x\). Wait, no, wait, maybe the original equation is \(11(4 - 2x)=-4(4x + 4)-2x\)? Wait, no, maybe the left side is \(11(4 - 2x)\) and right side is \(-4(4x + 4)-2x\). Wait, let's re - expand. Left side: \(11\times4-11\times2x = 44 - 22x\). Right side: \(-4\times4x-4\times4-2x=-16x - 16 - 2x=-18x - 16\). Then, \(44 - 22x=-18x - 16\). Add \(22x\) to both sides: \(44 = 4x - 16\). Add 16: \(60 = 4x\), so \(x = 15\). Wait, but the options have \(x = 15\) (yellow), \(x=-15\) (red), \(x = 1.5\) (blue). Wait, but maybe the original equation was written incorrectly? Wait, maybe the left side is \(1.1(4 - 2x)\) instead of \(11(4 - 2x)\)? Let's try that. If left side is \(1.1(4 - 2x)=4.4-2.2x\). Right side: \(-4(4x + 4)-2x=-16x - 16 - 2x=-18x - 16\). Then, \(4.4-2.2x=-18x - 16\). Add \(18x\) to both sides: \(4.4 + 15.8x=-16\). Subtract 4.4: \(15.8x=-20.4\), \(x=\frac{-20.4}{15.8}\approx - 1.29\), no. Wait, maybe the original equation is \(11(4 - 2x)=-4(4x - 4)-2x\)? Let's check. Left side: \(44-22x\). Right side: \(-16x + 16-2x=-18x + 16\). Then, \(44-22x=-18x + 16\). Add \(22x\): \(44 = 4x + 16\). Subtract 16: \(28 = 4x\), \(x = 7\). No. Wait, maybe the original equation is \(11(4 - 2x)=-4(4x + 4)-2x\), but the user made a typo. Wait, but according to the calculation with \(11(4 - 2x)\), we get \(x = 15\), which is the yellow option. But let's check the arithmetic again. Wait, \(44 - 22x=-18x - 16\). Add \(22x\) to both sides: \(44 = 4x - 16\). Add 16: \(60 = 4x\), \(x = 15\). So the solution is \(x = 15\), which is the yellow option.

Answer:

\(x = 15\) (yellow)