Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-2x+3)& = & 12 \color{red}{+} (3+x) \\\Leftrightarrow & -6x+9& = &12+3+x \\\Leftrightarrow & -6x \color{red}{+9} & = &15 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & -6x-x& = &15-9 \\\Leftrightarrow & -7x& = &6 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{6}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x-3)& = & 9 \color{red}{-} (9+x) \\\Leftrightarrow & 12x-12& = &9-9-x \\\Leftrightarrow & 12x \color{red}{-12} & = &0 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &0+12 \\\Leftrightarrow & 13x& = &12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (3x+2)& = & -5 \color{red}{-} (-10+x) \\\Leftrightarrow & 12x+8& = &-5+10-x \\\Leftrightarrow & 12x \color{red}{+8} & = &5 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 12x+x& = &5-8 \\\Leftrightarrow & 13x& = &-3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-6x+2)& = & -8 \color{red}{+} (-9-5x) \\\Leftrightarrow & -36x+12& = &-8-9-5x \\\Leftrightarrow & -36x \color{red}{+12} & = &-17 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & -36x+5x& = &-17-12 \\\Leftrightarrow & -31x& = &-29 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-29}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{29}{31} & & \\ & V = \left\{ \frac{29}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-3x+5)& = & 3 \color{red}{+} (4+x) \\\Leftrightarrow & -12x+20& = &3+4+x \\\Leftrightarrow & -12x \color{red}{+20} & = &7 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -12x-x& = &7-20 \\\Leftrightarrow & -13x& = &-13 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-13}{ \color{red}{-13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x-5)& = & 5 \color{red}{-} (-2+4x) \\\Leftrightarrow & 15x-25& = &5+2-4x \\\Leftrightarrow & 15x \color{red}{-25} & = &7 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{-25} \color{blue}{+25} \color{blue}{+4x} & = &7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+25} \\\Leftrightarrow & 15x+4x& = &7+25 \\\Leftrightarrow & 19x& = &32 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{32}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{32}{19} & & \\ & V = \left\{ \frac{32}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (3x+3)& = & -2 \color{red}{-} (11+x) \\\Leftrightarrow & 9x+9& = &-2-11-x \\\Leftrightarrow & 9x \color{red}{+9} & = &-13 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & 9x+x& = &-13-9 \\\Leftrightarrow & 10x& = &-22 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{-22}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{-11}{5} & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (4x+5)& = & -2 \color{red}{+} (11+x) \\\Leftrightarrow & 16x+20& = &-2+11+x \\\Leftrightarrow & 16x \color{red}{+20} & = &9 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 16x-x& = &9-20 \\\Leftrightarrow & 15x& = &-11 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{-11}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{-11}{15} & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-5x+7)& = & 9 \color{red}{-} (-11+2x) \\\Leftrightarrow & -25x+35& = &9+11-2x \\\Leftrightarrow & -25x \color{red}{+35} & = &20 \color{red}{-2x} \\\Leftrightarrow & -25x \color{red}{+35} \color{blue}{-35} \color{blue}{+2x} & = &20 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-35} \\\Leftrightarrow & -25x+2x& = &20-35 \\\Leftrightarrow & -23x& = &-15 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-15}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{15}{23} & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-5x-4)& = & 9 \color{red}{+} (2+x) \\\Leftrightarrow & -25x-20& = &9+2+x \\\Leftrightarrow & -25x \color{red}{-20} & = &11 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -25x-x& = &11+20 \\\Leftrightarrow & -26x& = &31 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{31}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{-31}{26} & & \\ & V = \left\{ \frac{-31}{26} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x-7)& = & -11 \color{red}{-} (-11+3x) \\\Leftrightarrow & -20x-28& = &-11+11-3x \\\Leftrightarrow & -20x \color{red}{-28} & = &0 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-28} \color{blue}{+28} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+28} \\\Leftrightarrow & -20x+3x& = &0+28 \\\Leftrightarrow & -17x& = &28 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{28}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-28}{17} & & \\ & V = \left\{ \frac{-28}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (6x-5)& = & 5 \color{red}{+} (-7+x) \\\Leftrightarrow & 12x-10& = &5-7+x \\\Leftrightarrow & 12x \color{red}{-10} & = &-2 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 12x-x& = &-2+10 \\\Leftrightarrow & 11x& = &8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)