Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x-1)& = & 13 \color{red}{+} (-2-5x) \\\Leftrightarrow & -18x-3& = &13-2-5x \\\Leftrightarrow & -18x \color{red}{-3} & = &11 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{+5x} & = &11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+3} \\\Leftrightarrow & -18x+5x& = &11+3 \\\Leftrightarrow & -13x& = &14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (5x-6)& = & -10 \color{red}{-} (9+x) \\\Leftrightarrow & 20x-24& = &-10-9-x \\\Leftrightarrow & 20x \color{red}{-24} & = &-19 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 20x+x& = &-19+24 \\\Leftrightarrow & 21x& = &5 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{5}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{5}{21} & & \\ & V = \left\{ \frac{5}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x-7)& = & -15 \color{red}{+} (-3-2x) \\\Leftrightarrow & 25x-35& = &-15-3-2x \\\Leftrightarrow & 25x \color{red}{-35} & = &-18 \color{red}{-2x} \\\Leftrightarrow & 25x \color{red}{-35} \color{blue}{+35} \color{blue}{+2x} & = &-18 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+35} \\\Leftrightarrow & 25x+2x& = &-18+35 \\\Leftrightarrow & 27x& = &17 \\\Leftrightarrow & \frac{27x}{ \color{red}{27} }& = &\frac{17}{ \color{red}{27} } \\\Leftrightarrow & x = \frac{17}{27} & & \\ & V = \left\{ \frac{17}{27} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-5x-4)& = & 15 \color{red}{-} (-2-4x) \\\Leftrightarrow & -25x-20& = &15+2+4x \\\Leftrightarrow & -25x \color{red}{-20} & = &17 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &17 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & -25x-4x& = &17+20 \\\Leftrightarrow & -29x& = &37 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{37}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-37}{29} & & \\ & V = \left\{ \frac{-37}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (x-2)& = & 3 \color{red}{-} (-5+x) \\\Leftrightarrow & 6x-12& = &3+5-x \\\Leftrightarrow & 6x \color{red}{-12} & = &8 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 6x+x& = &8+12 \\\Leftrightarrow & 7x& = &20 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{20}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{20}{7} & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-4x+4)& = & -10 \color{red}{-} (15+x) \\\Leftrightarrow & -8x+8& = &-10-15-x \\\Leftrightarrow & -8x \color{red}{+8} & = &-25 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -8x+x& = &-25-8 \\\Leftrightarrow & -7x& = &-33 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-33}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{33}{7} & & \\ & V = \left\{ \frac{33}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-4x-4)& = & -11 \color{red}{-} (7+x) \\\Leftrightarrow & -24x-24& = &-11-7-x \\\Leftrightarrow & -24x \color{red}{-24} & = &-18 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -24x+x& = &-18+24 \\\Leftrightarrow & -23x& = &6 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{6}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-6}{23} & & \\ & V = \left\{ \frac{-6}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x+1)& = & 6 \color{red}{+} (-3+x) \\\Leftrightarrow & 6x+6& = &6-3+x \\\Leftrightarrow & 6x \color{red}{+6} & = &3 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 6x-x& = &3-6 \\\Leftrightarrow & 5x& = &-3 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-3}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (6x-4)& = & 9 \color{red}{-} (15+x) \\\Leftrightarrow & 30x-20& = &9-15-x \\\Leftrightarrow & 30x \color{red}{-20} & = &-6 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 30x+x& = &-6+20 \\\Leftrightarrow & 31x& = &14 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{14}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{14}{31} & & \\ & V = \left\{ \frac{14}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x+6)& = & 3 \color{red}{-} (-13-3x) \\\Leftrightarrow & 10x+30& = &3+13+3x \\\Leftrightarrow & 10x \color{red}{+30} & = &16 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+30} \color{blue}{-30} \color{blue}{-3x} & = &16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-30} \\\Leftrightarrow & 10x-3x& = &16-30 \\\Leftrightarrow & 7x& = &-14 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-14}{ \color{red}{7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-x-6)& = & -11 \color{red}{-} (-8-5x) \\\Leftrightarrow & -6x-36& = &-11+8+5x \\\Leftrightarrow & -6x \color{red}{-36} & = &-3 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{-5x} & = &-3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+36} \\\Leftrightarrow & -6x-5x& = &-3+36 \\\Leftrightarrow & -11x& = &33 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{33}{ \color{red}{-11} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (5x+7)& = & 11 \color{red}{-} (-2+x) \\\Leftrightarrow & 20x+28& = &11+2-x \\\Leftrightarrow & 20x \color{red}{+28} & = &13 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 20x+x& = &13-28 \\\Leftrightarrow & 21x& = &-15 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-15}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)