Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (6x+5)& = & 9 \color{red}{-} (-1+x) \\\Leftrightarrow & 24x+20& = &9+1-x \\\Leftrightarrow & 24x \color{red}{+20} & = &10 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 24x+x& = &10-20 \\\Leftrightarrow & 25x& = &-10 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-10}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-2x+1)& = & 4 \color{red}{+} (-1+x) \\\Leftrightarrow & -12x+6& = &4-1+x \\\Leftrightarrow & -12x \color{red}{+6} & = &3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &3-6 \\\Leftrightarrow & -13x& = &-3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (5x+7)& = & -14 \color{red}{+} (-8+x) \\\Leftrightarrow & 30x+42& = &-14-8+x \\\Leftrightarrow & 30x \color{red}{+42} & = &-22 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 30x-x& = &-22-42 \\\Leftrightarrow & 29x& = &-64 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-64}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-64}{29} & & \\ & V = \left\{ \frac{-64}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x-5)& = & 1 \color{red}{-} (-12+x) \\\Leftrightarrow & 30x-30& = &1+12-x \\\Leftrightarrow & 30x \color{red}{-30} & = &13 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &13+30 \\\Leftrightarrow & 31x& = &43 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{43}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{43}{31} & & \\ & V = \left\{ \frac{43}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-x-2)& = & 9 \color{red}{+} (-4-5x) \\\Leftrightarrow & -6x-12& = &9-4-5x \\\Leftrightarrow & -6x \color{red}{-12} & = &5 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -6x+5x& = &5+12 \\\Leftrightarrow & -x& = &17 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{17}{ \color{red}{-1} } \\\Leftrightarrow & x = -17 & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (4x-4)& = & -14 \color{red}{-} (15+x) \\\Leftrightarrow & 24x-24& = &-14-15-x \\\Leftrightarrow & 24x \color{red}{-24} & = &-29 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-29 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 24x+x& = &-29+24 \\\Leftrightarrow & 25x& = &-5 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-5}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (4x+7)& = & 4 \color{red}{-} (7+x) \\\Leftrightarrow & 24x+42& = &4-7-x \\\Leftrightarrow & 24x \color{red}{+42} & = &-3 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 24x+x& = &-3-42 \\\Leftrightarrow & 25x& = &-45 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-45}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-9}{5} & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-3x+7)& = & -3 \color{red}{+} (-8+x) \\\Leftrightarrow & -12x+28& = &-3-8+x \\\Leftrightarrow & -12x \color{red}{+28} & = &-11 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -12x-x& = &-11-28 \\\Leftrightarrow & -13x& = &-39 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-39}{ \color{red}{-13} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (6x+4)& = & 1 \color{red}{+} (-9+x) \\\Leftrightarrow & 24x+16& = &1-9+x \\\Leftrightarrow & 24x \color{red}{+16} & = &-8 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 24x-x& = &-8-16 \\\Leftrightarrow & 23x& = &-24 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-24}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-24}{23} & & \\ & V = \left\{ \frac{-24}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x+4)& = & 11 \color{red}{-} (8+x) \\\Leftrightarrow & -36x+24& = &11-8-x \\\Leftrightarrow & -36x \color{red}{+24} & = &3 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -36x+x& = &3-24 \\\Leftrightarrow & -35x& = &-21 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-21}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x+4)& = & 12 \color{red}{-} (-8+x) \\\Leftrightarrow & -24x+16& = &12+8-x \\\Leftrightarrow & -24x \color{red}{+16} & = &20 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -24x+x& = &20-16 \\\Leftrightarrow & -23x& = &4 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{4}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-4}{23} & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-x+3)& = & 11 \color{red}{-} (6+x) \\\Leftrightarrow & -6x+18& = &11-6-x \\\Leftrightarrow & -6x \color{red}{+18} & = &5 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -6x+x& = &5-18 \\\Leftrightarrow & -5x& = &-13 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-13}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{13}{5} & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)