Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (6x-7)& = & -4 \color{red}{-} (3+x) \\\Leftrightarrow & 24x-28& = &-4-3-x \\\Leftrightarrow & 24x \color{red}{-28} & = &-7 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 24x+x& = &-7+28 \\\Leftrightarrow & 25x& = &21 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{21}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{21}{25} & & \\ & V = \left\{ \frac{21}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-4x+6)& = & 7 \color{red}{+} (-1-5x) \\\Leftrightarrow & -16x+24& = &7-1-5x \\\Leftrightarrow & -16x \color{red}{+24} & = &6 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & -16x+5x& = &6-24 \\\Leftrightarrow & -11x& = &-18 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-18}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{18}{11} & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-2x+3)& = & -4 \color{red}{+} (9+3x) \\\Leftrightarrow & -8x+12& = &-4+9+3x \\\Leftrightarrow & -8x \color{red}{+12} & = &5 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & -8x-3x& = &5-12 \\\Leftrightarrow & -11x& = &-7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (6x+6)& = & -8 \color{red}{-} (-7+x) \\\Leftrightarrow & 24x+24& = &-8+7-x \\\Leftrightarrow & 24x \color{red}{+24} & = &-1 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &-1-24 \\\Leftrightarrow & 25x& = &-25 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-25}{ \color{red}{25} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-5x+1)& = & -6 \color{red}{-} (-2+x) \\\Leftrightarrow & -20x+4& = &-6+2-x \\\Leftrightarrow & -20x \color{red}{+4} & = &-4 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -20x+x& = &-4-4 \\\Leftrightarrow & -19x& = &-8 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-8}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{8}{19} & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-5x-4)& = & -15 \color{red}{-} (6-4x) \\\Leftrightarrow & -25x-20& = &-15-6+4x \\\Leftrightarrow & -25x \color{red}{-20} & = &-21 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &-21 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & -25x-4x& = &-21+20 \\\Leftrightarrow & -29x& = &-1 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-1}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{1}{29} & & \\ & V = \left\{ \frac{1}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-6x-7)& = & -13 \color{red}{-} (-9+x) \\\Leftrightarrow & -36x-42& = &-13+9-x \\\Leftrightarrow & -36x \color{red}{-42} & = &-4 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -36x+x& = &-4+42 \\\Leftrightarrow & -35x& = &38 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{38}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{-38}{35} & & \\ & V = \left\{ \frac{-38}{35} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x+2)& = & -9 \color{red}{-} (9+3x) \\\Leftrightarrow & 2x+4& = &-9-9-3x \\\Leftrightarrow & 2x \color{red}{+4} & = &-18 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 2x+3x& = &-18-4 \\\Leftrightarrow & 5x& = &-22 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-22}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-22}{5} & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (2x+1)& = & -8 \color{red}{+} (11+x) \\\Leftrightarrow & 12x+6& = &-8+11+x \\\Leftrightarrow & 12x \color{red}{+6} & = &3 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &3-6 \\\Leftrightarrow & 11x& = &-3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-x-7)& = & -8 \color{red}{+} (7+x) \\\Leftrightarrow & -4x-28& = &-8+7+x \\\Leftrightarrow & -4x \color{red}{-28} & = &-1 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -4x-x& = &-1+28 \\\Leftrightarrow & -5x& = &27 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{27}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-27}{5} & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (5x+1)& = & -5 \color{red}{+} (14-2x) \\\Leftrightarrow & 15x+3& = &-5+14-2x \\\Leftrightarrow & 15x \color{red}{+3} & = &9 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+3} \color{blue}{-3} \color{blue}{+2x} & = &9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-3} \\\Leftrightarrow & 15x+2x& = &9-3 \\\Leftrightarrow & 17x& = &6 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{6}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (3x+2)& = & 1 \color{red}{+} (7-2x) \\\Leftrightarrow & 15x+10& = &1+7-2x \\\Leftrightarrow & 15x \color{red}{+10} & = &8 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+10} \color{blue}{-10} \color{blue}{+2x} & = &8 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-10} \\\Leftrightarrow & 15x+2x& = &8-10 \\\Leftrightarrow & 17x& = &-2 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-2}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-2}{17} & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)