Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (x-6)& = & 2 \color{red}{-} (8-3x) \\\Leftrightarrow & 4x-24& = &2-8+3x \\\Leftrightarrow & 4x \color{red}{-24} & = &-6 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-24} \color{blue}{+24} \color{blue}{-3x} & = &-6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+24} \\\Leftrightarrow & 4x-3x& = &-6+24 \\\Leftrightarrow & x& = &18 \\ & V = \left\{ 18 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-3x+7)& = & -12 \color{red}{-} (-1+x) \\\Leftrightarrow & -9x+21& = &-12+1-x \\\Leftrightarrow & -9x \color{red}{+21} & = &-11 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -9x+x& = &-11-21 \\\Leftrightarrow & -8x& = &-32 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{-32}{ \color{red}{-8} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (2x+3)& = & 11 \color{red}{-} (-8+x) \\\Leftrightarrow & 12x+18& = &11+8-x \\\Leftrightarrow & 12x \color{red}{+18} & = &19 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 12x+x& = &19-18 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-4x+3)& = & 6 \color{red}{-} (-15+x) \\\Leftrightarrow & -24x+18& = &6+15-x \\\Leftrightarrow & -24x \color{red}{+18} & = &21 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -24x+x& = &21-18 \\\Leftrightarrow & -23x& = &3 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{3}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (3x+2)& = & -8 \color{red}{+} (9+x) \\\Leftrightarrow & 18x+12& = &-8+9+x \\\Leftrightarrow & 18x \color{red}{+12} & = &1 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 18x-x& = &1-12 \\\Leftrightarrow & 17x& = &-11 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-11}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-11}{17} & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x+2)& = & 9 \color{red}{+} (14+x) \\\Leftrightarrow & -24x+8& = &9+14+x \\\Leftrightarrow & -24x \color{red}{+8} & = &23 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -24x-x& = &23-8 \\\Leftrightarrow & -25x& = &15 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{15}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-2x-4)& = & 9 \color{red}{-} (7+3x) \\\Leftrightarrow & -4x-8& = &9-7-3x \\\Leftrightarrow & -4x \color{red}{-8} & = &2 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -4x+3x& = &2+8 \\\Leftrightarrow & -x& = &10 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{10}{ \color{red}{-1} } \\\Leftrightarrow & x = -10 & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (x+3)& = & -1 \color{red}{-} (-4-3x) \\\Leftrightarrow & 4x+12& = &-1+4+3x \\\Leftrightarrow & 4x \color{red}{+12} & = &3 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 4x-3x& = &3-12 \\\Leftrightarrow & x& = &-9 \\ & V = \left\{ -9 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-3x+7)& = & 5 \color{red}{-} (8+x) \\\Leftrightarrow & -6x+14& = &5-8-x \\\Leftrightarrow & -6x \color{red}{+14} & = &-3 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -6x+x& = &-3-14 \\\Leftrightarrow & -5x& = &-17 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-17}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{17}{5} & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (4x+4)& = & 5 \color{red}{-} (14+x) \\\Leftrightarrow & 24x+24& = &5-14-x \\\Leftrightarrow & 24x \color{red}{+24} & = &-9 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &-9-24 \\\Leftrightarrow & 25x& = &-33 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-33}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-33}{25} & & \\ & V = \left\{ \frac{-33}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x-1)& = & 3 \color{red}{+} (-15-5x) \\\Leftrightarrow & 18x-3& = &3-15-5x \\\Leftrightarrow & 18x \color{red}{-3} & = &-12 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{+5x} & = &-12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+3} \\\Leftrightarrow & 18x+5x& = &-12+3 \\\Leftrightarrow & 23x& = &-9 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-9}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-9}{23} & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-x-4)& = & 15 \color{red}{+} (-14-3x) \\\Leftrightarrow & -4x-16& = &15-14-3x \\\Leftrightarrow & -4x \color{red}{-16} & = &1 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & -4x+3x& = &1+16 \\\Leftrightarrow & -x& = &17 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{17}{ \color{red}{-1} } \\\Leftrightarrow & x = -17 & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)