Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (2x+1)& = & -1 \color{red}{-} (-5+x) \\\Leftrightarrow & 4x+2& = &-1+5-x \\\Leftrightarrow & 4x \color{red}{+2} & = &4 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 4x+x& = &4-2 \\\Leftrightarrow & 5x& = &2 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{2}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-5x-5)& = & -7 \color{red}{+} (6+x) \\\Leftrightarrow & -20x-20& = &-7+6+x \\\Leftrightarrow & -20x \color{red}{-20} & = &-1 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -20x-x& = &-1+20 \\\Leftrightarrow & -21x& = &19 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{19}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-19}{21} & & \\ & V = \left\{ \frac{-19}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-2x-4)& = & -10 \color{red}{+} (1+x) \\\Leftrightarrow & -6x-12& = &-10+1+x \\\Leftrightarrow & -6x \color{red}{-12} & = &-9 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -6x-x& = &-9+12 \\\Leftrightarrow & -7x& = &3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-4x+7)& = & 15 \color{red}{-} (-15+x) \\\Leftrightarrow & -24x+42& = &15+15-x \\\Leftrightarrow & -24x \color{red}{+42} & = &30 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &30 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -24x+x& = &30-42 \\\Leftrightarrow & -23x& = &-12 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-12}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{12}{23} & & \\ & V = \left\{ \frac{12}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-5x+6)& = & 11 \color{red}{+} (-8+x) \\\Leftrightarrow & -30x+36& = &11-8+x \\\Leftrightarrow & -30x \color{red}{+36} & = &3 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -30x-x& = &3-36 \\\Leftrightarrow & -31x& = &-33 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-33}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{33}{31} & & \\ & V = \left\{ \frac{33}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (5x+1)& = & 7 \color{red}{+} (14-4x) \\\Leftrightarrow & 25x+5& = &7+14-4x \\\Leftrightarrow & 25x \color{red}{+5} & = &21 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{+4x} & = &21 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-5} \\\Leftrightarrow & 25x+4x& = &21-5 \\\Leftrightarrow & 29x& = &16 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{16}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{16}{29} & & \\ & V = \left\{ \frac{16}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (6x-6)& = & -10 \color{red}{+} (-15+x) \\\Leftrightarrow & 24x-24& = &-10-15+x \\\Leftrightarrow & 24x \color{red}{-24} & = &-25 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 24x-x& = &-25+24 \\\Leftrightarrow & 23x& = &-1 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-1}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-1}{23} & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (2x-4)& = & -9 \color{red}{-} (-12+x) \\\Leftrightarrow & 12x-24& = &-9+12-x \\\Leftrightarrow & 12x \color{red}{-24} & = &3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 12x+x& = &3+24 \\\Leftrightarrow & 13x& = &27 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{27}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{27}{13} & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-4x-1)& = & -10 \color{red}{-} (-10+x) \\\Leftrightarrow & -8x-2& = &-10+10-x \\\Leftrightarrow & -8x \color{red}{-2} & = &0 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -8x+x& = &0+2 \\\Leftrightarrow & -7x& = &2 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{2}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x-7)& = & 3 \color{red}{-} (-13+x) \\\Leftrightarrow & -36x-42& = &3+13-x \\\Leftrightarrow & -36x \color{red}{-42} & = &16 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -36x+x& = &16+42 \\\Leftrightarrow & -35x& = &58 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{58}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{-58}{35} & & \\ & V = \left\{ \frac{-58}{35} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (5x-2)& = & 10 \color{red}{-} (11+x) \\\Leftrightarrow & 30x-12& = &10-11-x \\\Leftrightarrow & 30x \color{red}{-12} & = &-1 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 30x+x& = &-1+12 \\\Leftrightarrow & 31x& = &11 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{11}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{11}{31} & & \\ & V = \left\{ \frac{11}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-2x+1)& = & -1 \color{red}{+} (-15+3x) \\\Leftrightarrow & -4x+2& = &-1-15+3x \\\Leftrightarrow & -4x \color{red}{+2} & = &-16 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & -4x-3x& = &-16-2 \\\Leftrightarrow & -7x& = &-18 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-18}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{18}{7} & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)