Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x-6)& = & -10 \color{red}{-} (8-3x) \\\Leftrightarrow & 10x-12& = &-10-8+3x \\\Leftrightarrow & 10x \color{red}{-12} & = &-18 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &-18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & 10x-3x& = &-18+12 \\\Leftrightarrow & 7x& = &-6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (2x-3)& = & -1 \color{red}{-} (8+x) \\\Leftrightarrow & 6x-9& = &-1-8-x \\\Leftrightarrow & 6x \color{red}{-9} & = &-9 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 6x+x& = &-9+9 \\\Leftrightarrow & 7x& = &0 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{0}{ \color{red}{7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x-1)& = & -1 \color{red}{+} (-10+x) \\\Leftrightarrow & -12x-4& = &-1-10+x \\\Leftrightarrow & -12x \color{red}{-4} & = &-11 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -12x-x& = &-11+4 \\\Leftrightarrow & -13x& = &-7 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-7}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-x-7)& = & -14 \color{red}{+} (-11+x) \\\Leftrightarrow & -2x-14& = &-14-11+x \\\Leftrightarrow & -2x \color{red}{-14} & = &-25 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -2x-x& = &-25+14 \\\Leftrightarrow & -3x& = &-11 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-11}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{11}{3} & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x-7)& = & -1 \color{red}{-} (-8+x) \\\Leftrightarrow & -24x-28& = &-1+8-x \\\Leftrightarrow & -24x \color{red}{-28} & = &7 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -24x+x& = &7+28 \\\Leftrightarrow & -23x& = &35 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{35}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-35}{23} & & \\ & V = \left\{ \frac{-35}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x+7)& = & -7 \color{red}{+} (-3+x) \\\Leftrightarrow & 5x+35& = &-7-3+x \\\Leftrightarrow & 5x \color{red}{+35} & = &-10 \color{red}{+x} \\\Leftrightarrow & 5x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 5x-x& = &-10-35 \\\Leftrightarrow & 4x& = &-45 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-45}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{-45}{4} & & \\ & V = \left\{ \frac{-45}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-5x+6)& = & -10 \color{red}{-} (-15+x) \\\Leftrightarrow & -30x+36& = &-10+15-x \\\Leftrightarrow & -30x \color{red}{+36} & = &5 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -30x+x& = &5-36 \\\Leftrightarrow & -29x& = &-31 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-31}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{31}{29} & & \\ & V = \left\{ \frac{31}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x-7)& = & 14 \color{red}{+} (-1+x) \\\Leftrightarrow & -15x-21& = &14-1+x \\\Leftrightarrow & -15x \color{red}{-21} & = &13 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & -15x-x& = &13+21 \\\Leftrightarrow & -16x& = &34 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{34}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-17}{8} & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x-2)& = & 13 \color{red}{+} (-13+x) \\\Leftrightarrow & 9x-6& = &13-13+x \\\Leftrightarrow & 9x \color{red}{-6} & = &0 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 9x-x& = &0+6 \\\Leftrightarrow & 8x& = &6 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{6}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{3}{4} & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-4x+3)& = & -15 \color{red}{+} (9+x) \\\Leftrightarrow & -20x+15& = &-15+9+x \\\Leftrightarrow & -20x \color{red}{+15} & = &-6 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -20x-x& = &-6-15 \\\Leftrightarrow & -21x& = &-21 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-21}{ \color{red}{-21} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-5x+2)& = & -11 \color{red}{-} (1+x) \\\Leftrightarrow & -10x+4& = &-11-1-x \\\Leftrightarrow & -10x \color{red}{+4} & = &-12 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -10x+x& = &-12-4 \\\Leftrightarrow & -9x& = &-16 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-16}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{16}{9} & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-3x+2)& = & 10 \color{red}{+} (-15+x) \\\Leftrightarrow & -15x+10& = &10-15+x \\\Leftrightarrow & -15x \color{red}{+10} & = &-5 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -15x-x& = &-5-10 \\\Leftrightarrow & -16x& = &-15 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-15}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{15}{16} & & \\ & V = \left\{ \frac{15}{16} \right\} & \\\end{align}\)