Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-4x+1)& = & -1 \color{red}{+} (-9+x) \\\Leftrightarrow & -8x+2& = &-1-9+x \\\Leftrightarrow & -8x \color{red}{+2} & = &-10 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & -8x-x& = &-10-2 \\\Leftrightarrow & -9x& = &-12 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-12}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-6x-2)& = & -15 \color{red}{+} (-13+x) \\\Leftrightarrow & -24x-8& = &-15-13+x \\\Leftrightarrow & -24x \color{red}{-8} & = &-28 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-28 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -24x-x& = &-28+8 \\\Leftrightarrow & -25x& = &-20 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-20}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (5x+6)& = & -10 \color{red}{-} (4+x) \\\Leftrightarrow & 30x+36& = &-10-4-x \\\Leftrightarrow & 30x \color{red}{+36} & = &-14 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 30x+x& = &-14-36 \\\Leftrightarrow & 31x& = &-50 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-50}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-50}{31} & & \\ & V = \left\{ \frac{-50}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x+2)& = & 4 \color{red}{+} (11+x) \\\Leftrightarrow & 30x+12& = &4+11+x \\\Leftrightarrow & 30x \color{red}{+12} & = &15 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 30x-x& = &15-12 \\\Leftrightarrow & 29x& = &3 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{3}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{3}{29} & & \\ & V = \left\{ \frac{3}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (5x-7)& = & -10 \color{red}{+} (-6+x) \\\Leftrightarrow & 30x-42& = &-10-6+x \\\Leftrightarrow & 30x \color{red}{-42} & = &-16 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 30x-x& = &-16+42 \\\Leftrightarrow & 29x& = &26 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{26}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{26}{29} & & \\ & V = \left\{ \frac{26}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-3x-6)& = & 10 \color{red}{-} (12-2x) \\\Leftrightarrow & -9x-18& = &10-12+2x \\\Leftrightarrow & -9x \color{red}{-18} & = &-2 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{-18} \color{blue}{+18} \color{blue}{-2x} & = &-2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+18} \\\Leftrightarrow & -9x-2x& = &-2+18 \\\Leftrightarrow & -11x& = &16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-3x+2)& = & -5 \color{red}{+} (8-2x) \\\Leftrightarrow & -15x+10& = &-5+8-2x \\\Leftrightarrow & -15x \color{red}{+10} & = &3 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+10} \color{blue}{-10} \color{blue}{+2x} & = &3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-10} \\\Leftrightarrow & -15x+2x& = &3-10 \\\Leftrightarrow & -13x& = &-7 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-7}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (4x-2)& = & -15 \color{red}{+} (4+x) \\\Leftrightarrow & 8x-4& = &-15+4+x \\\Leftrightarrow & 8x \color{red}{-4} & = &-11 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 8x-x& = &-11+4 \\\Leftrightarrow & 7x& = &-7 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-7}{ \color{red}{7} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x-1)& = & 7 \color{red}{+} (-11-5x) \\\Leftrightarrow & 3x-3& = &7-11-5x \\\Leftrightarrow & 3x \color{red}{-3} & = &-4 \color{red}{-5x} \\\Leftrightarrow & 3x \color{red}{-3} \color{blue}{+3} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+3} \\\Leftrightarrow & 3x+5x& = &-4+3 \\\Leftrightarrow & 8x& = &-1 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-1}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-1}{8} & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-3x+2)& = & -12 \color{red}{-} (-12+x) \\\Leftrightarrow & -12x+8& = &-12+12-x \\\Leftrightarrow & -12x \color{red}{+8} & = &0 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &0-8 \\\Leftrightarrow & -11x& = &-8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-x-1)& = & 8 \color{red}{+} (-13+x) \\\Leftrightarrow & -6x-6& = &8-13+x \\\Leftrightarrow & -6x \color{red}{-6} & = &-5 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -6x-x& = &-5+6 \\\Leftrightarrow & -7x& = &1 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{1}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (3x+7)& = & -11 \color{red}{+} (-12+x) \\\Leftrightarrow & 18x+42& = &-11-12+x \\\Leftrightarrow & 18x \color{red}{+42} & = &-23 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 18x-x& = &-23-42 \\\Leftrightarrow & 17x& = &-65 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-65}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-65}{17} & & \\ & V = \left\{ \frac{-65}{17} \right\} & \\\end{align}\)