Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-x-1)& = & -6 \color{red}{-} (12-4x) \\\Leftrightarrow & -5x-5& = &-6-12+4x \\\Leftrightarrow & -5x \color{red}{-5} & = &-18 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-5} \color{blue}{+5} \color{blue}{-4x} & = &-18 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+5} \\\Leftrightarrow & -5x-4x& = &-18+5 \\\Leftrightarrow & -9x& = &-13 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-13}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{13}{9} & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-2x+7)& = & -7 \color{red}{-} (3+x) \\\Leftrightarrow & -12x+42& = &-7-3-x \\\Leftrightarrow & -12x \color{red}{+42} & = &-10 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -12x+x& = &-10-42 \\\Leftrightarrow & -11x& = &-52 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-52}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{52}{11} & & \\ & V = \left\{ \frac{52}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-4x-1)& = & -7 \color{red}{+} (12+x) \\\Leftrightarrow & -24x-6& = &-7+12+x \\\Leftrightarrow & -24x \color{red}{-6} & = &5 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -24x-x& = &5+6 \\\Leftrightarrow & -25x& = &11 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{11}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-11}{25} & & \\ & V = \left\{ \frac{-11}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-4x+3)& = & 12 \color{red}{+} (3+x) \\\Leftrightarrow & -24x+18& = &12+3+x \\\Leftrightarrow & -24x \color{red}{+18} & = &15 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -24x-x& = &15-18 \\\Leftrightarrow & -25x& = &-3 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-3}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{3}{25} & & \\ & V = \left\{ \frac{3}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x-1)& = & 3 \color{red}{+} (-14+4x) \\\Leftrightarrow & 3x-3& = &3-14+4x \\\Leftrightarrow & 3x \color{red}{-3} & = &-11 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{-3} \color{blue}{+3} \color{blue}{-4x} & = &-11 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+3} \\\Leftrightarrow & 3x-4x& = &-11+3 \\\Leftrightarrow & -x& = &-8 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-8}{ \color{red}{-1} } \\\Leftrightarrow & x = 8 & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-5x-3)& = & 7 \color{red}{-} (3+x) \\\Leftrightarrow & -30x-18& = &7-3-x \\\Leftrightarrow & -30x \color{red}{-18} & = &4 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -30x+x& = &4+18 \\\Leftrightarrow & -29x& = &22 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{22}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-22}{29} & & \\ & V = \left\{ \frac{-22}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (6x-4)& = & -12 \color{red}{-} (-2+x) \\\Leftrightarrow & 12x-8& = &-12+2-x \\\Leftrightarrow & 12x \color{red}{-8} & = &-10 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 12x+x& = &-10+8 \\\Leftrightarrow & 13x& = &-2 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-2}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (4x-4)& = & 10 \color{red}{-} (-2+x) \\\Leftrightarrow & 12x-12& = &10+2-x \\\Leftrightarrow & 12x \color{red}{-12} & = &12 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &12+12 \\\Leftrightarrow & 13x& = &24 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{24}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-3x+3)& = & -2 \color{red}{+} (10+x) \\\Leftrightarrow & -18x+18& = &-2+10+x \\\Leftrightarrow & -18x \color{red}{+18} & = &8 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -18x-x& = &8-18 \\\Leftrightarrow & -19x& = &-10 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-10}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{10}{19} & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-5x+5)& = & 1 \color{red}{-} (-11-3x) \\\Leftrightarrow & -25x+25& = &1+11+3x \\\Leftrightarrow & -25x \color{red}{+25} & = &12 \color{red}{+3x} \\\Leftrightarrow & -25x \color{red}{+25} \color{blue}{-25} \color{blue}{-3x} & = &12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-25} \\\Leftrightarrow & -25x-3x& = &12-25 \\\Leftrightarrow & -28x& = &-13 \\\Leftrightarrow & \frac{-28x}{ \color{red}{-28} }& = &\frac{-13}{ \color{red}{-28} } \\\Leftrightarrow & x = \frac{13}{28} & & \\ & V = \left\{ \frac{13}{28} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (3x-6)& = & 3 \color{red}{-} (-5+2x) \\\Leftrightarrow & 9x-18& = &3+5-2x \\\Leftrightarrow & 9x \color{red}{-18} & = &8 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &8 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & 9x+2x& = &8+18 \\\Leftrightarrow & 11x& = &26 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{26}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{26}{11} & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (6x-7)& = & 10 \color{red}{+} (-14+x) \\\Leftrightarrow & 24x-28& = &10-14+x \\\Leftrightarrow & 24x \color{red}{-28} & = &-4 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 24x-x& = &-4+28 \\\Leftrightarrow & 23x& = &24 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{24}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{24}{23} & & \\ & V = \left\{ \frac{24}{23} \right\} & \\\end{align}\)