Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-2x+3)& = & 12 \color{red}{+} (-9+x) \\\Leftrightarrow & -12x+18& = &12-9+x \\\Leftrightarrow & -12x \color{red}{+18} & = &3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -12x-x& = &3-18 \\\Leftrightarrow & -13x& = &-15 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-15}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (4x+5)& = & 10 \color{red}{-} (-7+x) \\\Leftrightarrow & 8x+10& = &10+7-x \\\Leftrightarrow & 8x \color{red}{+10} & = &17 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 8x+x& = &17-10 \\\Leftrightarrow & 9x& = &7 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{7}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{7}{9} & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-3x-7)& = & -3 \color{red}{+} (-6-5x) \\\Leftrightarrow & -6x-14& = &-3-6-5x \\\Leftrightarrow & -6x \color{red}{-14} & = &-9 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-14} \color{blue}{+14} \color{blue}{+5x} & = &-9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+14} \\\Leftrightarrow & -6x+5x& = &-9+14 \\\Leftrightarrow & -x& = &5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{5}{ \color{red}{-1} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-3x+3)& = & -6 \color{red}{-} (14+x) \\\Leftrightarrow & -15x+15& = &-6-14-x \\\Leftrightarrow & -15x \color{red}{+15} & = &-20 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -15x+x& = &-20-15 \\\Leftrightarrow & -14x& = &-35 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-35}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{5}{2} & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-4x+5)& = & -7 \color{red}{-} (-7+x) \\\Leftrightarrow & -12x+15& = &-7+7-x \\\Leftrightarrow & -12x \color{red}{+15} & = &0 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -12x+x& = &0-15 \\\Leftrightarrow & -11x& = &-15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{15}{11} & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (4x-1)& = & 3 \color{red}{+} (-3+x) \\\Leftrightarrow & 12x-3& = &3-3+x \\\Leftrightarrow & 12x \color{red}{-3} & = &0 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 12x-x& = &0+3 \\\Leftrightarrow & 11x& = &3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (2x-3)& = & 2 \color{red}{-} (-14-3x) \\\Leftrightarrow & 4x-6& = &2+14+3x \\\Leftrightarrow & 4x \color{red}{-6} & = &16 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-6} \color{blue}{+6} \color{blue}{-3x} & = &16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+6} \\\Leftrightarrow & 4x-3x& = &16+6 \\\Leftrightarrow & x& = &22 \\ & V = \left\{ 22 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (4x+3)& = & -4 \color{red}{-} (7+x) \\\Leftrightarrow & 20x+15& = &-4-7-x \\\Leftrightarrow & 20x \color{red}{+15} & = &-11 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 20x+x& = &-11-15 \\\Leftrightarrow & 21x& = &-26 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-26}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-26}{21} & & \\ & V = \left\{ \frac{-26}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-2x+1)& = & -1 \color{red}{-} (2-5x) \\\Leftrightarrow & -6x+3& = &-1-2+5x \\\Leftrightarrow & -6x \color{red}{+3} & = &-3 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+3} \color{blue}{-3} \color{blue}{-5x} & = &-3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-3} \\\Leftrightarrow & -6x-5x& = &-3-3 \\\Leftrightarrow & -11x& = &-6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-x-6)& = & 8 \color{red}{-} (7-3x) \\\Leftrightarrow & -4x-24& = &8-7+3x \\\Leftrightarrow & -4x \color{red}{-24} & = &1 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-24} \color{blue}{+24} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+24} \\\Leftrightarrow & -4x-3x& = &1+24 \\\Leftrightarrow & -7x& = &25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-6x+3)& = & 7 \color{red}{-} (8+x) \\\Leftrightarrow & -30x+15& = &7-8-x \\\Leftrightarrow & -30x \color{red}{+15} & = &-1 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -30x+x& = &-1-15 \\\Leftrightarrow & -29x& = &-16 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-16}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{16}{29} & & \\ & V = \left\{ \frac{16}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-x+2)& = & -7 \color{red}{-} (-14+x) \\\Leftrightarrow & -2x+4& = &-7+14-x \\\Leftrightarrow & -2x \color{red}{+4} & = &7 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -2x+x& = &7-4 \\\Leftrightarrow & -x& = &3 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{3}{ \color{red}{-1} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)