Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x-7)& = & 6 \color{red}{-} (1+x) \\\Leftrightarrow & -30x-42& = &6-1-x \\\Leftrightarrow & -30x \color{red}{-42} & = &5 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -30x+x& = &5+42 \\\Leftrightarrow & -29x& = &47 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{47}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-47}{29} & & \\ & V = \left\{ \frac{-47}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (5x+5)& = & -15 \color{red}{+} (15+x) \\\Leftrightarrow & 30x+30& = &-15+15+x \\\Leftrightarrow & 30x \color{red}{+30} & = &0 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 30x-x& = &0-30 \\\Leftrightarrow & 29x& = &-30 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-30}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-30}{29} & & \\ & V = \left\{ \frac{-30}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x-1)& = & -14 \color{red}{-} (10-5x) \\\Leftrightarrow & 18x-3& = &-14-10+5x \\\Leftrightarrow & 18x \color{red}{-3} & = &-24 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &-24 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 18x-5x& = &-24+3 \\\Leftrightarrow & 13x& = &-21 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-21}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-21}{13} & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (5x+3)& = & 4 \color{red}{-} (2+x) \\\Leftrightarrow & 10x+6& = &4-2-x \\\Leftrightarrow & 10x \color{red}{+6} & = &2 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 10x+x& = &2-6 \\\Leftrightarrow & 11x& = &-4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x+1)& = & 12 \color{red}{+} (-14+x) \\\Leftrightarrow & -18x+3& = &12-14+x \\\Leftrightarrow & -18x \color{red}{+3} & = &-2 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -18x-x& = &-2-3 \\\Leftrightarrow & -19x& = &-5 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-5}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{5}{19} & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-3x-2)& = & -8 \color{red}{-} (10-2x) \\\Leftrightarrow & -9x-6& = &-8-10+2x \\\Leftrightarrow & -9x \color{red}{-6} & = &-18 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{-2x} & = &-18 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+6} \\\Leftrightarrow & -9x-2x& = &-18+6 \\\Leftrightarrow & -11x& = &-12 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-12}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-4x+6)& = & -12 \color{red}{+} (7+x) \\\Leftrightarrow & -24x+36& = &-12+7+x \\\Leftrightarrow & -24x \color{red}{+36} & = &-5 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -24x-x& = &-5-36 \\\Leftrightarrow & -25x& = &-41 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-41}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{41}{25} & & \\ & V = \left\{ \frac{41}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-3x+5)& = & -4 \color{red}{-} (-2-5x) \\\Leftrightarrow & -18x+30& = &-4+2+5x \\\Leftrightarrow & -18x \color{red}{+30} & = &-2 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+30} \color{blue}{-30} \color{blue}{-5x} & = &-2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-30} \\\Leftrightarrow & -18x-5x& = &-2-30 \\\Leftrightarrow & -23x& = &-32 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-32}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{32}{23} & & \\ & V = \left\{ \frac{32}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-6x-4)& = & -8 \color{red}{-} (-3+x) \\\Leftrightarrow & -12x-8& = &-8+3-x \\\Leftrightarrow & -12x \color{red}{-8} & = &-5 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -12x+x& = &-5+8 \\\Leftrightarrow & -11x& = &3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-3x-4)& = & 13 \color{red}{+} (-10+x) \\\Leftrightarrow & -18x-24& = &13-10+x \\\Leftrightarrow & -18x \color{red}{-24} & = &3 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -18x-x& = &3+24 \\\Leftrightarrow & -19x& = &27 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{27}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-27}{19} & & \\ & V = \left\{ \frac{-27}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (2x-5)& = & 2 \color{red}{+} (3-3x) \\\Leftrightarrow & 10x-25& = &2+3-3x \\\Leftrightarrow & 10x \color{red}{-25} & = &5 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-25} \color{blue}{+25} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+25} \\\Leftrightarrow & 10x+3x& = &5+25 \\\Leftrightarrow & 13x& = &30 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{30}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{30}{13} & & \\ & V = \left\{ \frac{30}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (4x-2)& = & 3 \color{red}{-} (5+x) \\\Leftrightarrow & 20x-10& = &3-5-x \\\Leftrightarrow & 20x \color{red}{-10} & = &-2 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 20x+x& = &-2+10 \\\Leftrightarrow & 21x& = &8 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{8}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{8}{21} & & \\ & V = \left\{ \frac{8}{21} \right\} & \\\end{align}\)