Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-2x-1)& = & -2 \color{red}{-} (4+x) \\\Leftrightarrow & -6x-3& = &-2-4-x \\\Leftrightarrow & -6x \color{red}{-3} & = &-6 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -6x+x& = &-6+3 \\\Leftrightarrow & -5x& = &-3 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-3}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-6x+5)& = & -13 \color{red}{-} (-9-5x) \\\Leftrightarrow & -18x+15& = &-13+9+5x \\\Leftrightarrow & -18x \color{red}{+15} & = &-4 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+15} \color{blue}{-15} \color{blue}{-5x} & = &-4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-15} \\\Leftrightarrow & -18x-5x& = &-4-15 \\\Leftrightarrow & -23x& = &-19 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-19}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{19}{23} & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x-7)& = & -9 \color{red}{-} (2+x) \\\Leftrightarrow & 12x-21& = &-9-2-x \\\Leftrightarrow & 12x \color{red}{-21} & = &-11 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & 12x+x& = &-11+21 \\\Leftrightarrow & 13x& = &10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (3x+4)& = & 5 \color{red}{-} (11+x) \\\Leftrightarrow & 12x+16& = &5-11-x \\\Leftrightarrow & 12x \color{red}{+16} & = &-6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 12x+x& = &-6-16 \\\Leftrightarrow & 13x& = &-22 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-22}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (x+6)& = & -11 \color{red}{+} (13+3x) \\\Leftrightarrow & 2x+12& = &-11+13+3x \\\Leftrightarrow & 2x \color{red}{+12} & = &2 \color{red}{+3x} \\\Leftrightarrow & 2x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 2x-3x& = &2-12 \\\Leftrightarrow & -x& = &-10 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-10}{ \color{red}{-1} } \\\Leftrightarrow & x = 10 & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (3x+4)& = & 1 \color{red}{+} (-13+x) \\\Leftrightarrow & 6x+8& = &1-13+x \\\Leftrightarrow & 6x \color{red}{+8} & = &-12 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 6x-x& = &-12-8 \\\Leftrightarrow & 5x& = &-20 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-20}{ \color{red}{5} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-3x-6)& = & 6 \color{red}{-} (8+x) \\\Leftrightarrow & -12x-24& = &6-8-x \\\Leftrightarrow & -12x \color{red}{-24} & = &-2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -12x+x& = &-2+24 \\\Leftrightarrow & -11x& = &22 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{22}{ \color{red}{-11} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (3x-6)& = & 14 \color{red}{-} (1+x) \\\Leftrightarrow & 12x-24& = &14-1-x \\\Leftrightarrow & 12x \color{red}{-24} & = &13 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 12x+x& = &13+24 \\\Leftrightarrow & 13x& = &37 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{37}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{37}{13} & & \\ & V = \left\{ \frac{37}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (5x-1)& = & -4 \color{red}{+} (14+3x) \\\Leftrightarrow & 20x-4& = &-4+14+3x \\\Leftrightarrow & 20x \color{red}{-4} & = &10 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 20x-3x& = &10+4 \\\Leftrightarrow & 17x& = &14 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{14}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{14}{17} & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (2x+6)& = & -4 \color{red}{+} (10+x) \\\Leftrightarrow & 12x+36& = &-4+10+x \\\Leftrightarrow & 12x \color{red}{+36} & = &6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 12x-x& = &6-36 \\\Leftrightarrow & 11x& = &-30 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-30}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-30}{11} & & \\ & V = \left\{ \frac{-30}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (5x-6)& = & -7 \color{red}{-} (4+x) \\\Leftrightarrow & 15x-18& = &-7-4-x \\\Leftrightarrow & 15x \color{red}{-18} & = &-11 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 15x+x& = &-11+18 \\\Leftrightarrow & 16x& = &7 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{7}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{7}{16} & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (5x+1)& = & 12 \color{red}{-} (-13+x) \\\Leftrightarrow & 20x+4& = &12+13-x \\\Leftrightarrow & 20x \color{red}{+4} & = &25 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 20x+x& = &25-4 \\\Leftrightarrow & 21x& = &21 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{21}{ \color{red}{21} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)