Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (3x+3)& = & 14 \color{red}{+} (3+x) \\\Leftrightarrow & 12x+12& = &14+3+x \\\Leftrightarrow & 12x \color{red}{+12} & = &17 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &17-12 \\\Leftrightarrow & 11x& = &5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-5x+4)& = & -8 \color{red}{+} (2+x) \\\Leftrightarrow & -15x+12& = &-8+2+x \\\Leftrightarrow & -15x \color{red}{+12} & = &-6 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -15x-x& = &-6-12 \\\Leftrightarrow & -16x& = &-18 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-18}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{9}{8} & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (5x+3)& = & -15 \color{red}{+} (-6+x) \\\Leftrightarrow & 20x+12& = &-15-6+x \\\Leftrightarrow & 20x \color{red}{+12} & = &-21 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 20x-x& = &-21-12 \\\Leftrightarrow & 19x& = &-33 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-33}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-33}{19} & & \\ & V = \left\{ \frac{-33}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (3x-3)& = & -7 \color{red}{-} (-7+x) \\\Leftrightarrow & 18x-18& = &-7+7-x \\\Leftrightarrow & 18x \color{red}{-18} & = &0 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 18x+x& = &0+18 \\\Leftrightarrow & 19x& = &18 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{18}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{18}{19} & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (4x-1)& = & -3 \color{red}{-} (8-5x) \\\Leftrightarrow & 16x-4& = &-3-8+5x \\\Leftrightarrow & 16x \color{red}{-4} & = &-11 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{-4} \color{blue}{+4} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+4} \\\Leftrightarrow & 16x-5x& = &-11+4 \\\Leftrightarrow & 11x& = &-7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (4x+1)& = & 5 \color{red}{-} (-2+x) \\\Leftrightarrow & 24x+6& = &5+2-x \\\Leftrightarrow & 24x \color{red}{+6} & = &7 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 24x+x& = &7-6 \\\Leftrightarrow & 25x& = &1 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{1}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{1}{25} & & \\ & V = \left\{ \frac{1}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x-6)& = & -13 \color{red}{+} (-1+x) \\\Leftrightarrow & -12x-36& = &-13-1+x \\\Leftrightarrow & -12x \color{red}{-36} & = &-14 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -12x-x& = &-14+36 \\\Leftrightarrow & -13x& = &22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-4x+7)& = & 15 \color{red}{+} (13+x) \\\Leftrightarrow & -24x+42& = &15+13+x \\\Leftrightarrow & -24x \color{red}{+42} & = &28 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &28 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -24x-x& = &28-42 \\\Leftrightarrow & -25x& = &-14 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-14}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{14}{25} & & \\ & V = \left\{ \frac{14}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (3x-1)& = & 10 \color{red}{+} (-2+x) \\\Leftrightarrow & 12x-4& = &10-2+x \\\Leftrightarrow & 12x \color{red}{-4} & = &8 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 12x-x& = &8+4 \\\Leftrightarrow & 11x& = &12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (x-5)& = & 12 \color{red}{+} (-12+4x) \\\Leftrightarrow & 3x-15& = &12-12+4x \\\Leftrightarrow & 3x \color{red}{-15} & = &0 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{-15} \color{blue}{+15} \color{blue}{-4x} & = &0 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+15} \\\Leftrightarrow & 3x-4x& = &0+15 \\\Leftrightarrow & -x& = &15 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{15}{ \color{red}{-1} } \\\Leftrightarrow & x = -15 & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (2x-4)& = & -12 \color{red}{-} (-6+x) \\\Leftrightarrow & 4x-8& = &-12+6-x \\\Leftrightarrow & 4x \color{red}{-8} & = &-6 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 4x+x& = &-6+8 \\\Leftrightarrow & 5x& = &2 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{2}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (4x+7)& = & 11 \color{red}{-} (-9+x) \\\Leftrightarrow & 8x+14& = &11+9-x \\\Leftrightarrow & 8x \color{red}{+14} & = &20 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 8x+x& = &20-14 \\\Leftrightarrow & 9x& = &6 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{6}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)