Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x-7)& = & 5 \color{red}{-} (8-5x) \\\Leftrightarrow & -18x-21& = &5-8+5x \\\Leftrightarrow & -18x \color{red}{-21} & = &-3 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-21} \color{blue}{+21} \color{blue}{-5x} & = &-3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+21} \\\Leftrightarrow & -18x-5x& = &-3+21 \\\Leftrightarrow & -23x& = &18 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{18}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-18}{23} & & \\ & V = \left\{ \frac{-18}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-2x+5)& = & 2 \color{red}{+} (4+x) \\\Leftrightarrow & -4x+10& = &2+4+x \\\Leftrightarrow & -4x \color{red}{+10} & = &6 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -4x-x& = &6-10 \\\Leftrightarrow & -5x& = &-4 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-4}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-4x-4)& = & -9 \color{red}{+} (-1+x) \\\Leftrightarrow & -12x-12& = &-9-1+x \\\Leftrightarrow & -12x \color{red}{-12} & = &-10 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &-10+12 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-4x+6)& = & 8 \color{red}{+} (12+x) \\\Leftrightarrow & -20x+30& = &8+12+x \\\Leftrightarrow & -20x \color{red}{+30} & = &20 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -20x-x& = &20-30 \\\Leftrightarrow & -21x& = &-10 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-10}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{10}{21} & & \\ & V = \left\{ \frac{10}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-3x+4)& = & 4 \color{red}{+} (7-2x) \\\Leftrightarrow & -15x+20& = &4+7-2x \\\Leftrightarrow & -15x \color{red}{+20} & = &11 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & -15x+2x& = &11-20 \\\Leftrightarrow & -13x& = &-9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-3x+6)& = & 13 \color{red}{-} (-5+x) \\\Leftrightarrow & -12x+24& = &13+5-x \\\Leftrightarrow & -12x \color{red}{+24} & = &18 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -12x+x& = &18-24 \\\Leftrightarrow & -11x& = &-6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (6x-5)& = & 13 \color{red}{+} (4+x) \\\Leftrightarrow & 24x-20& = &13+4+x \\\Leftrightarrow & 24x \color{red}{-20} & = &17 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 24x-x& = &17+20 \\\Leftrightarrow & 23x& = &37 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{37}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{37}{23} & & \\ & V = \left\{ \frac{37}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (4x-6)& = & -6 \color{red}{-} (-5-5x) \\\Leftrightarrow & 8x-12& = &-6+5+5x \\\Leftrightarrow & 8x \color{red}{-12} & = &-1 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 8x-5x& = &-1+12 \\\Leftrightarrow & 3x& = &11 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{11}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{11}{3} & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x-4)& = & -14 \color{red}{+} (-15+x) \\\Leftrightarrow & 18x-24& = &-14-15+x \\\Leftrightarrow & 18x \color{red}{-24} & = &-29 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-29 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 18x-x& = &-29+24 \\\Leftrightarrow & 17x& = &-5 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-5}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-5}{17} & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (4x+3)& = & -14 \color{red}{+} (7+x) \\\Leftrightarrow & 16x+12& = &-14+7+x \\\Leftrightarrow & 16x \color{red}{+12} & = &-7 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 16x-x& = &-7-12 \\\Leftrightarrow & 15x& = &-19 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{-19}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{-19}{15} & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x+1)& = & -3 \color{red}{-} (-13+x) \\\Leftrightarrow & -12x+6& = &-3+13-x \\\Leftrightarrow & -12x \color{red}{+6} & = &10 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -12x+x& = &10-6 \\\Leftrightarrow & -11x& = &4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x-7)& = & 11 \color{red}{+} (-13+x) \\\Leftrightarrow & -30x-35& = &11-13+x \\\Leftrightarrow & -30x \color{red}{-35} & = &-2 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & -30x-x& = &-2+35 \\\Leftrightarrow & -31x& = &33 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{33}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-33}{31} & & \\ & V = \left\{ \frac{-33}{31} \right\} & \\\end{align}\)