Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-6x+2)& = & 11 \color{red}{+} (6-5x) \\\Leftrightarrow & -36x+12& = &11+6-5x \\\Leftrightarrow & -36x \color{red}{+12} & = &17 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & -36x+5x& = &17-12 \\\Leftrightarrow & -31x& = &5 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{5}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-5}{31} & & \\ & V = \left\{ \frac{-5}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x-5)& = & -5 \color{red}{-} (2-4x) \\\Leftrightarrow & 25x-25& = &-5-2+4x \\\Leftrightarrow & 25x \color{red}{-25} & = &-7 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{-25} \color{blue}{+25} \color{blue}{-4x} & = &-7 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+25} \\\Leftrightarrow & 25x-4x& = &-7+25 \\\Leftrightarrow & 21x& = &18 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{18}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x-1)& = & -10 \color{red}{+} (5+x) \\\Leftrightarrow & -12x-4& = &-10+5+x \\\Leftrightarrow & -12x \color{red}{-4} & = &-5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -12x-x& = &-5+4 \\\Leftrightarrow & -13x& = &-1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (3x-2)& = & -13 \color{red}{-} (-6+x) \\\Leftrightarrow & 15x-10& = &-13+6-x \\\Leftrightarrow & 15x \color{red}{-10} & = &-7 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 15x+x& = &-7+10 \\\Leftrightarrow & 16x& = &3 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{3}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{3}{16} & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-x+1)& = & -4 \color{red}{-} (7+x) \\\Leftrightarrow & -2x+2& = &-4-7-x \\\Leftrightarrow & -2x \color{red}{+2} & = &-11 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -2x+x& = &-11-2 \\\Leftrightarrow & -x& = &-13 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-13}{ \color{red}{-1} } \\\Leftrightarrow & x = 13 & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x+6)& = & -2 \color{red}{-} (2+x) \\\Leftrightarrow & -24x+24& = &-2-2-x \\\Leftrightarrow & -24x \color{red}{+24} & = &-4 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -24x+x& = &-4-24 \\\Leftrightarrow & -23x& = &-28 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-28}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{28}{23} & & \\ & V = \left\{ \frac{28}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x-1)& = & 8 \color{red}{+} (-9+x) \\\Leftrightarrow & -30x-5& = &8-9+x \\\Leftrightarrow & -30x \color{red}{-5} & = &-1 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & -30x-x& = &-1+5 \\\Leftrightarrow & -31x& = &4 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{4}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-4}{31} & & \\ & V = \left\{ \frac{-4}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (2x+2)& = & -12 \color{red}{+} (-4+3x) \\\Leftrightarrow & 4x+4& = &-12-4+3x \\\Leftrightarrow & 4x \color{red}{+4} & = &-16 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &-16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & 4x-3x& = &-16-4 \\\Leftrightarrow & x& = &-20 \\ & V = \left\{ -20 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (5x-2)& = & 15 \color{red}{-} (-14-3x) \\\Leftrightarrow & 10x-4& = &15+14+3x \\\Leftrightarrow & 10x \color{red}{-4} & = &29 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &29 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 10x-3x& = &29+4 \\\Leftrightarrow & 7x& = &33 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{33}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{33}{7} & & \\ & V = \left\{ \frac{33}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (5x+6)& = & 3 \color{red}{+} (-3+3x) \\\Leftrightarrow & 20x+24& = &3-3+3x \\\Leftrightarrow & 20x \color{red}{+24} & = &0 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & 20x-3x& = &0-24 \\\Leftrightarrow & 17x& = &-24 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-24}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-24}{17} & & \\ & V = \left\{ \frac{-24}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (5x+2)& = & -12 \color{red}{-} (-1+4x) \\\Leftrightarrow & 15x+6& = &-12+1-4x \\\Leftrightarrow & 15x \color{red}{+6} & = &-11 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+6} \color{blue}{-6} \color{blue}{+4x} & = &-11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-6} \\\Leftrightarrow & 15x+4x& = &-11-6 \\\Leftrightarrow & 19x& = &-17 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-17}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-17}{19} & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-5x-2)& = & -6 \color{red}{+} (-15-3x) \\\Leftrightarrow & -10x-4& = &-6-15-3x \\\Leftrightarrow & -10x \color{red}{-4} & = &-21 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &-21 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -10x+3x& = &-21+4 \\\Leftrightarrow & -7x& = &-17 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-17}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)