Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-4x-2)& = & -15 \color{red}{-} (-5+3x) \\\Leftrightarrow & -8x-4& = &-15+5-3x \\\Leftrightarrow & -8x \color{red}{-4} & = &-10 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &-10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -8x+3x& = &-10+4 \\\Leftrightarrow & -5x& = &-6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x-4)& = & -12 \color{red}{+} (-8-4x) \\\Leftrightarrow & 25x-20& = &-12-8-4x \\\Leftrightarrow & 25x \color{red}{-20} & = &-20 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{-20} \color{blue}{+20} \color{blue}{+4x} & = &-20 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+20} \\\Leftrightarrow & 25x+4x& = &-20+20 \\\Leftrightarrow & 29x& = &0 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{0}{ \color{red}{29} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-4x-3)& = & 3 \color{red}{-} (14+x) \\\Leftrightarrow & -12x-9& = &3-14-x \\\Leftrightarrow & -12x \color{red}{-9} & = &-11 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & -12x+x& = &-11+9 \\\Leftrightarrow & -11x& = &-2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-5x+1)& = & -7 \color{red}{-} (11-2x) \\\Leftrightarrow & -15x+3& = &-7-11+2x \\\Leftrightarrow & -15x \color{red}{+3} & = &-18 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &-18 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & -15x-2x& = &-18-3 \\\Leftrightarrow & -17x& = &-21 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-21}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{21}{17} & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-5x-4)& = & -15 \color{red}{-} (-6+x) \\\Leftrightarrow & -20x-16& = &-15+6-x \\\Leftrightarrow & -20x \color{red}{-16} & = &-9 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -20x+x& = &-9+16 \\\Leftrightarrow & -19x& = &7 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{7}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-7}{19} & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (6x-3)& = & 11 \color{red}{-} (8+x) \\\Leftrightarrow & 12x-6& = &11-8-x \\\Leftrightarrow & 12x \color{red}{-6} & = &3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 12x+x& = &3+6 \\\Leftrightarrow & 13x& = &9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (2x+6)& = & 15 \color{red}{-} (-6-3x) \\\Leftrightarrow & 4x+12& = &15+6+3x \\\Leftrightarrow & 4x \color{red}{+12} & = &21 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &21 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 4x-3x& = &21-12 \\\Leftrightarrow & x& = &9 \\ & V = \left\{ 9 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (6x+4)& = & 6 \color{red}{+} (11-5x) \\\Leftrightarrow & 36x+24& = &6+11-5x \\\Leftrightarrow & 36x \color{red}{+24} & = &17 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & 36x+5x& = &17-24 \\\Leftrightarrow & 41x& = &-7 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-7}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{-7}{41} & & \\ & V = \left\{ \frac{-7}{41} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x-2)& = & 5 \color{red}{-} (-6-4x) \\\Leftrightarrow & 9x-6& = &5+6+4x \\\Leftrightarrow & 9x \color{red}{-6} & = &11 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-6} \color{blue}{+6} \color{blue}{-4x} & = &11 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+6} \\\Leftrightarrow & 9x-4x& = &11+6 \\\Leftrightarrow & 5x& = &17 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{17}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{17}{5} & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x-2)& = & 1 \color{red}{-} (-8-5x) \\\Leftrightarrow & -16x-8& = &1+8+5x \\\Leftrightarrow & -16x \color{red}{-8} & = &9 \color{red}{+5x} \\\Leftrightarrow & -16x \color{red}{-8} \color{blue}{+8} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+8} \\\Leftrightarrow & -16x-5x& = &9+8 \\\Leftrightarrow & -21x& = &17 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{17}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-17}{21} & & \\ & V = \left\{ \frac{-17}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (6x-1)& = & -15 \color{red}{+} (-5+x) \\\Leftrightarrow & 24x-4& = &-15-5+x \\\Leftrightarrow & 24x \color{red}{-4} & = &-20 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 24x-x& = &-20+4 \\\Leftrightarrow & 23x& = &-16 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-16}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-16}{23} & & \\ & V = \left\{ \frac{-16}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (3x+1)& = & -6 \color{red}{-} (2+x) \\\Leftrightarrow & 9x+3& = &-6-2-x \\\Leftrightarrow & 9x \color{red}{+3} & = &-8 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 9x+x& = &-8-3 \\\Leftrightarrow & 10x& = &-11 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{-11}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{-11}{10} & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)