Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(2(-6x-5)=-12-(-4+x)\)
2. \(6(-6x+2)=-7-(3+x)\)
3. \(4(2x+4)=-14-(-4+x)\)
4. \(2(x+5)=1-(8+x)\)
5. \(5(-4x-1)=5-(-11+x)\)
6. \(6(2x-7)=11+(8+x)\)
7. \(3(-2x+1)=-9+(15-5x)\)
8. \(3(2x-1)=7-(9+x)\)
9. \(4(-3x+3)=-11-(-10+x)\)
10. \(2(6x-6)=-11-(-13+x)\)
11. \(6(x+2)=14+(-12+x)\)
12. \(2(-4x-3)=11+(7+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x-5)& = & -12 \color{red}{-} (-4+x) \\\Leftrightarrow & -12x-10& = &-12+4-x \\\Leftrightarrow & -12x \color{red}{-10} & = &-8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -12x+x& = &-8+10 \\\Leftrightarrow & -11x& = &2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-6x+2)& = & -7 \color{red}{-} (3+x) \\\Leftrightarrow & -36x+12& = &-7-3-x \\\Leftrightarrow & -36x \color{red}{+12} & = &-10 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -36x+x& = &-10-12 \\\Leftrightarrow & -35x& = &-22 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-22}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{22}{35} & & \\ & V = \left\{ \frac{22}{35} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (2x+4)& = & -14 \color{red}{-} (-4+x) \\\Leftrightarrow & 8x+16& = &-14+4-x \\\Leftrightarrow & 8x \color{red}{+16} & = &-10 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 8x+x& = &-10-16 \\\Leftrightarrow & 9x& = &-26 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-26}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-26}{9} & & \\ & V = \left\{ \frac{-26}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x+5)& = & 1 \color{red}{-} (8+x) \\\Leftrightarrow & 2x+10& = &1-8-x \\\Leftrightarrow & 2x \color{red}{+10} & = &-7 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 2x+x& = &-7-10 \\\Leftrightarrow & 3x& = &-17 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-17}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-17}{3} & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-4x-1)& = & 5 \color{red}{-} (-11+x) \\\Leftrightarrow & -20x-5& = &5+11-x \\\Leftrightarrow & -20x \color{red}{-5} & = &16 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -20x+x& = &16+5 \\\Leftrightarrow & -19x& = &21 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{21}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-21}{19} & & \\ & V = \left\{ \frac{-21}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (2x-7)& = & 11 \color{red}{+} (8+x) \\\Leftrightarrow & 12x-42& = &11+8+x \\\Leftrightarrow & 12x \color{red}{-42} & = &19 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 12x-x& = &19+42 \\\Leftrightarrow & 11x& = &61 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{61}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{61}{11} & & \\ & V = \left\{ \frac{61}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-2x+1)& = & -9 \color{red}{+} (15-5x) \\\Leftrightarrow & -6x+3& = &-9+15-5x \\\Leftrightarrow & -6x \color{red}{+3} & = &6 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+3} \color{blue}{-3} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-3} \\\Leftrightarrow & -6x+5x& = &6-3 \\\Leftrightarrow & -x& = &3 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{3}{ \color{red}{-1} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (2x-1)& = & 7 \color{red}{-} (9+x) \\\Leftrightarrow & 6x-3& = &7-9-x \\\Leftrightarrow & 6x \color{red}{-3} & = &-2 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 6x+x& = &-2+3 \\\Leftrightarrow & 7x& = &1 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{1}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-3x+3)& = & -11 \color{red}{-} (-10+x) \\\Leftrightarrow & -12x+12& = &-11+10-x \\\Leftrightarrow & -12x \color{red}{+12} & = &-1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &-1-12 \\\Leftrightarrow & -11x& = &-13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (6x-6)& = & -11 \color{red}{-} (-13+x) \\\Leftrightarrow & 12x-12& = &-11+13-x \\\Leftrightarrow & 12x \color{red}{-12} & = &2 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &2+12 \\\Leftrightarrow & 13x& = &14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (x+2)& = & 14 \color{red}{+} (-12+x) \\\Leftrightarrow & 6x+12& = &14-12+x \\\Leftrightarrow & 6x \color{red}{+12} & = &2 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 6x-x& = &2-12 \\\Leftrightarrow & 5x& = &-10 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-10}{ \color{red}{5} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-4x-3)& = & 11 \color{red}{+} (7+x) \\\Leftrightarrow & -8x-6& = &11+7+x \\\Leftrightarrow & -8x \color{red}{-6} & = &18 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -8x-x& = &18+6 \\\Leftrightarrow & -9x& = &24 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{24}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-8}{3} & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)