Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-x-3)& = & 3 \color{red}{+} (9-5x) \\\Leftrightarrow & -3x-9& = &3+9-5x \\\Leftrightarrow & -3x \color{red}{-9} & = &12 \color{red}{-5x} \\\Leftrightarrow & -3x \color{red}{-9} \color{blue}{+9} \color{blue}{+5x} & = &12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+9} \\\Leftrightarrow & -3x+5x& = &12+9 \\\Leftrightarrow & 2x& = &21 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{21}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{21}{2} & & \\ & V = \left\{ \frac{21}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (4x-4)& = & 9 \color{red}{-} (-2+x) \\\Leftrightarrow & 12x-12& = &9+2-x \\\Leftrightarrow & 12x \color{red}{-12} & = &11 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &11+12 \\\Leftrightarrow & 13x& = &23 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{23}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{23}{13} & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (3x-6)& = & -11 \color{red}{-} (-5+x) \\\Leftrightarrow & 12x-24& = &-11+5-x \\\Leftrightarrow & 12x \color{red}{-24} & = &-6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 12x+x& = &-6+24 \\\Leftrightarrow & 13x& = &18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (4x-7)& = & -4 \color{red}{-} (5+x) \\\Leftrightarrow & 24x-42& = &-4-5-x \\\Leftrightarrow & 24x \color{red}{-42} & = &-9 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 24x+x& = &-9+42 \\\Leftrightarrow & 25x& = &33 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{33}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{33}{25} & & \\ & V = \left\{ \frac{33}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x-7)& = & -8 \color{red}{+} (-5-2x) \\\Leftrightarrow & -3x-21& = &-8-5-2x \\\Leftrightarrow & -3x \color{red}{-21} & = &-13 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{-21} \color{blue}{+21} \color{blue}{+2x} & = &-13 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+21} \\\Leftrightarrow & -3x+2x& = &-13+21 \\\Leftrightarrow & -x& = &8 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{8}{ \color{red}{-1} } \\\Leftrightarrow & x = -8 & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (4x+4)& = & -13 \color{red}{-} (7+x) \\\Leftrightarrow & 24x+24& = &-13-7-x \\\Leftrightarrow & 24x \color{red}{+24} & = &-20 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &-20-24 \\\Leftrightarrow & 25x& = &-44 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-44}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-44}{25} & & \\ & V = \left\{ \frac{-44}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-6x+5)& = & -13 \color{red}{-} (7+x) \\\Leftrightarrow & -12x+10& = &-13-7-x \\\Leftrightarrow & -12x \color{red}{+10} & = &-20 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -12x+x& = &-20-10 \\\Leftrightarrow & -11x& = &-30 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-30}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{30}{11} & & \\ & V = \left\{ \frac{30}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-2x+5)& = & -11 \color{red}{+} (13+x) \\\Leftrightarrow & -10x+25& = &-11+13+x \\\Leftrightarrow & -10x \color{red}{+25} & = &2 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -10x-x& = &2-25 \\\Leftrightarrow & -11x& = &-23 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-23}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{23}{11} & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (5x-4)& = & 13 \color{red}{+} (8+x) \\\Leftrightarrow & 25x-20& = &13+8+x \\\Leftrightarrow & 25x \color{red}{-20} & = &21 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 25x-x& = &21+20 \\\Leftrightarrow & 24x& = &41 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{41}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{41}{24} & & \\ & V = \left\{ \frac{41}{24} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-3x+3)& = & 3 \color{red}{-} (2-5x) \\\Leftrightarrow & -18x+18& = &3-2+5x \\\Leftrightarrow & -18x \color{red}{+18} & = &1 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & -18x-5x& = &1-18 \\\Leftrightarrow & -23x& = &-17 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-17}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{17}{23} & & \\ & V = \left\{ \frac{17}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (5x+2)& = & -6 \color{red}{+} (-7+2x) \\\Leftrightarrow & 25x+10& = &-6-7+2x \\\Leftrightarrow & 25x \color{red}{+10} & = &-13 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{+10} \color{blue}{-10} \color{blue}{-2x} & = &-13 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-10} \\\Leftrightarrow & 25x-2x& = &-13-10 \\\Leftrightarrow & 23x& = &-23 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-23}{ \color{red}{23} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (3x-2)& = & 12 \color{red}{-} (-1+x) \\\Leftrightarrow & 12x-8& = &12+1-x \\\Leftrightarrow & 12x \color{red}{-8} & = &13 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 12x+x& = &13+8 \\\Leftrightarrow & 13x& = &21 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{21}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{21}{13} & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)