Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-6x+7)& = & -8 \color{red}{+} (-4+x) \\\Leftrightarrow & -24x+28& = &-8-4+x \\\Leftrightarrow & -24x \color{red}{+28} & = &-12 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -24x-x& = &-12-28 \\\Leftrightarrow & -25x& = &-40 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-40}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{8}{5} & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-2x-1)& = & 4 \color{red}{+} (-1+x) \\\Leftrightarrow & -12x-6& = &4-1+x \\\Leftrightarrow & -12x \color{red}{-6} & = &3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -12x-x& = &3+6 \\\Leftrightarrow & -13x& = &9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-x-1)& = & -3 \color{red}{-} (-7-2x) \\\Leftrightarrow & -3x-3& = &-3+7+2x \\\Leftrightarrow & -3x \color{red}{-3} & = &4 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-3} \color{blue}{+3} \color{blue}{-2x} & = &4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+3} \\\Leftrightarrow & -3x-2x& = &4+3 \\\Leftrightarrow & -5x& = &7 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{7}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (3x+2)& = & -3 \color{red}{-} (-14+x) \\\Leftrightarrow & 15x+10& = &-3+14-x \\\Leftrightarrow & 15x \color{red}{+10} & = &11 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 15x+x& = &11-10 \\\Leftrightarrow & 16x& = &1 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{1}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{1}{16} & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x+6)& = & 12 \color{red}{+} (14+x) \\\Leftrightarrow & 12x+24& = &12+14+x \\\Leftrightarrow & 12x \color{red}{+24} & = &26 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &26 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 12x-x& = &26-24 \\\Leftrightarrow & 11x& = &2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (3x-4)& = & 7 \color{red}{-} (5-5x) \\\Leftrightarrow & 18x-24& = &7-5+5x \\\Leftrightarrow & 18x \color{red}{-24} & = &2 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & 18x-5x& = &2+24 \\\Leftrightarrow & 13x& = &26 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{26}{ \color{red}{13} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x+7)& = & 2 \color{red}{+} (-14+x) \\\Leftrightarrow & -12x+42& = &2-14+x \\\Leftrightarrow & -12x \color{red}{+42} & = &-12 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -12x-x& = &-12-42 \\\Leftrightarrow & -13x& = &-54 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-54}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{54}{13} & & \\ & V = \left\{ \frac{54}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x-7)& = & 1 \color{red}{+} (3+x) \\\Leftrightarrow & 6x-42& = &1+3+x \\\Leftrightarrow & 6x \color{red}{-42} & = &4 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 6x-x& = &4+42 \\\Leftrightarrow & 5x& = &46 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{46}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{46}{5} & & \\ & V = \left\{ \frac{46}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (3x-7)& = & -12 \color{red}{-} (-9+x) \\\Leftrightarrow & 12x-28& = &-12+9-x \\\Leftrightarrow & 12x \color{red}{-28} & = &-3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 12x+x& = &-3+28 \\\Leftrightarrow & 13x& = &25 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{25}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{25}{13} & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (x+4)& = & -1 \color{red}{+} (-11-5x) \\\Leftrightarrow & 3x+12& = &-1-11-5x \\\Leftrightarrow & 3x \color{red}{+12} & = &-12 \color{red}{-5x} \\\Leftrightarrow & 3x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 3x+5x& = &-12-12 \\\Leftrightarrow & 8x& = &-24 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-24}{ \color{red}{8} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (4x-2)& = & -6 \color{red}{-} (-14+x) \\\Leftrightarrow & 12x-6& = &-6+14-x \\\Leftrightarrow & 12x \color{red}{-6} & = &8 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 12x+x& = &8+6 \\\Leftrightarrow & 13x& = &14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (4x+5)& = & -9 \color{red}{-} (9+x) \\\Leftrightarrow & 20x+25& = &-9-9-x \\\Leftrightarrow & 20x \color{red}{+25} & = &-18 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & 20x+x& = &-18-25 \\\Leftrightarrow & 21x& = &-43 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-43}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-43}{21} & & \\ & V = \left\{ \frac{-43}{21} \right\} & \\\end{align}\)