Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-3x-7)& = & 15 \color{red}{-} (-10-5x) \\\Leftrightarrow & -18x-42& = &15+10+5x \\\Leftrightarrow & -18x \color{red}{-42} & = &25 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-42} \color{blue}{+42} \color{blue}{-5x} & = &25 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+42} \\\Leftrightarrow & -18x-5x& = &25+42 \\\Leftrightarrow & -23x& = &67 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{67}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-67}{23} & & \\ & V = \left\{ \frac{-67}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-3x-1)& = & -13 \color{red}{+} (-6+x) \\\Leftrightarrow & -18x-6& = &-13-6+x \\\Leftrightarrow & -18x \color{red}{-6} & = &-19 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -18x-x& = &-19+6 \\\Leftrightarrow & -19x& = &-13 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-13}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{13}{19} & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x+1)& = & 3 \color{red}{-} (-7+x) \\\Leftrightarrow & 12x+3& = &3+7-x \\\Leftrightarrow & 12x \color{red}{+3} & = &10 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 12x+x& = &10-3 \\\Leftrightarrow & 13x& = &7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-2x-4)& = & 10 \color{red}{+} (-2-3x) \\\Leftrightarrow & -4x-8& = &10-2-3x \\\Leftrightarrow & -4x \color{red}{-8} & = &8 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -4x+3x& = &8+8 \\\Leftrightarrow & -x& = &16 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{16}{ \color{red}{-1} } \\\Leftrightarrow & x = -16 & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (6x+1)& = & -10 \color{red}{+} (-3+x) \\\Leftrightarrow & 12x+2& = &-10-3+x \\\Leftrightarrow & 12x \color{red}{+2} & = &-13 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & 12x-x& = &-13-2 \\\Leftrightarrow & 11x& = &-15 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-15}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-15}{11} & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x+3)& = & -9 \color{red}{+} (14+x) \\\Leftrightarrow & 15x+15& = &-9+14+x \\\Leftrightarrow & 15x \color{red}{+15} & = &5 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 15x-x& = &5-15 \\\Leftrightarrow & 14x& = &-10 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-10}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (2x+1)& = & 12 \color{red}{-} (5+x) \\\Leftrightarrow & 12x+6& = &12-5-x \\\Leftrightarrow & 12x \color{red}{+6} & = &7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 12x+x& = &7-6 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x+6)& = & 1 \color{red}{-} (-8+x) \\\Leftrightarrow & 24x+36& = &1+8-x \\\Leftrightarrow & 24x \color{red}{+36} & = &9 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 24x+x& = &9-36 \\\Leftrightarrow & 25x& = &-27 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-27}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-27}{25} & & \\ & V = \left\{ \frac{-27}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-x+6)& = & 11 \color{red}{+} (9-5x) \\\Leftrightarrow & -3x+18& = &11+9-5x \\\Leftrightarrow & -3x \color{red}{+18} & = &20 \color{red}{-5x} \\\Leftrightarrow & -3x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &20 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & -3x+5x& = &20-18 \\\Leftrightarrow & 2x& = &2 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{2}{ \color{red}{2} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (x+3)& = & -3 \color{red}{+} (-9-5x) \\\Leftrightarrow & 6x+18& = &-3-9-5x \\\Leftrightarrow & 6x \color{red}{+18} & = &-12 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &-12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 6x+5x& = &-12-18 \\\Leftrightarrow & 11x& = &-30 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-30}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-30}{11} & & \\ & V = \left\{ \frac{-30}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (6x-1)& = & 4 \color{red}{-} (-11+x) \\\Leftrightarrow & 12x-2& = &4+11-x \\\Leftrightarrow & 12x \color{red}{-2} & = &15 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 12x+x& = &15+2 \\\Leftrightarrow & 13x& = &17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (2x+6)& = & -7 \color{red}{+} (-1+x) \\\Leftrightarrow & 8x+24& = &-7-1+x \\\Leftrightarrow & 8x \color{red}{+24} & = &-8 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 8x-x& = &-8-24 \\\Leftrightarrow & 7x& = &-32 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-32}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-32}{7} & & \\ & V = \left\{ \frac{-32}{7} \right\} & \\\end{align}\)