Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x+2)& = & 15 \color{red}{+} (-7+x) \\\Leftrightarrow & -18x+6& = &15-7+x \\\Leftrightarrow & -18x \color{red}{+6} & = &8 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -18x-x& = &8-6 \\\Leftrightarrow & -19x& = &2 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{2}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-2}{19} & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-4x+3)& = & 2 \color{red}{+} (7+3x) \\\Leftrightarrow & -20x+15& = &2+7+3x \\\Leftrightarrow & -20x \color{red}{+15} & = &9 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{+15} \color{blue}{-15} \color{blue}{-3x} & = &9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-15} \\\Leftrightarrow & -20x-3x& = &9-15 \\\Leftrightarrow & -23x& = &-6 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-6}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{6}{23} & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x+2)& = & 4 \color{red}{+} (-5+x) \\\Leftrightarrow & -10x+4& = &4-5+x \\\Leftrightarrow & -10x \color{red}{+4} & = &-1 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -10x-x& = &-1-4 \\\Leftrightarrow & -11x& = &-5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x-1)& = & -2 \color{red}{+} (8+x) \\\Leftrightarrow & 9x-3& = &-2+8+x \\\Leftrightarrow & 9x \color{red}{-3} & = &6 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 9x-x& = &6+3 \\\Leftrightarrow & 8x& = &9 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{9}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{9}{8} & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-3x-4)& = & 1 \color{red}{-} (6-5x) \\\Leftrightarrow & -18x-24& = &1-6+5x \\\Leftrightarrow & -18x \color{red}{-24} & = &-5 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &-5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & -18x-5x& = &-5+24 \\\Leftrightarrow & -23x& = &19 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{19}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-19}{23} & & \\ & V = \left\{ \frac{-19}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-5x+4)& = & 15 \color{red}{+} (-13+x) \\\Leftrightarrow & -30x+24& = &15-13+x \\\Leftrightarrow & -30x \color{red}{+24} & = &2 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -30x-x& = &2-24 \\\Leftrightarrow & -31x& = &-22 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-22}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{22}{31} & & \\ & V = \left\{ \frac{22}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (3x+3)& = & -14 \color{red}{+} (11-2x) \\\Leftrightarrow & 9x+9& = &-14+11-2x \\\Leftrightarrow & 9x \color{red}{+9} & = &-3 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+9} \color{blue}{-9} \color{blue}{+2x} & = &-3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-9} \\\Leftrightarrow & 9x+2x& = &-3-9 \\\Leftrightarrow & 11x& = &-12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-x-3)& = & 8 \color{red}{+} (2+x) \\\Leftrightarrow & -3x-9& = &8+2+x \\\Leftrightarrow & -3x \color{red}{-9} & = &10 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & -3x-x& = &10+9 \\\Leftrightarrow & -4x& = &19 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{19}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-19}{4} & & \\ & V = \left\{ \frac{-19}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x-1)& = & 3 \color{red}{+} (14+x) \\\Leftrightarrow & 24x-6& = &3+14+x \\\Leftrightarrow & 24x \color{red}{-6} & = &17 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 24x-x& = &17+6 \\\Leftrightarrow & 23x& = &23 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{23}{ \color{red}{23} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (5x-4)& = & 13 \color{red}{-} (12+x) \\\Leftrightarrow & 20x-16& = &13-12-x \\\Leftrightarrow & 20x \color{red}{-16} & = &1 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 20x+x& = &1+16 \\\Leftrightarrow & 21x& = &17 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{17}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{17}{21} & & \\ & V = \left\{ \frac{17}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (x+7)& = & 3 \color{red}{+} (11+x) \\\Leftrightarrow & 2x+14& = &3+11+x \\\Leftrightarrow & 2x \color{red}{+14} & = &14 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 2x-x& = &14-14 \\\Leftrightarrow & x& = &0 \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-5x-2)& = & -15 \color{red}{+} (-8+x) \\\Leftrightarrow & -30x-12& = &-15-8+x \\\Leftrightarrow & -30x \color{red}{-12} & = &-23 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -30x-x& = &-23+12 \\\Leftrightarrow & -31x& = &-11 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-11}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{11}{31} & & \\ & V = \left\{ \frac{11}{31} \right\} & \\\end{align}\)