Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-4x+1)& = & 8 \color{red}{-} (-14-5x) \\\Leftrightarrow & -8x+2& = &8+14+5x \\\Leftrightarrow & -8x \color{red}{+2} & = &22 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+2} \color{blue}{-2} \color{blue}{-5x} & = &22 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-2} \\\Leftrightarrow & -8x-5x& = &22-2 \\\Leftrightarrow & -13x& = &20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (x+2)& = & -4 \color{red}{-} (9+x) \\\Leftrightarrow & 2x+4& = &-4-9-x \\\Leftrightarrow & 2x \color{red}{+4} & = &-13 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 2x+x& = &-13-4 \\\Leftrightarrow & 3x& = &-17 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-17}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-17}{3} & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (3x+2)& = & 10 \color{red}{-} (2+x) \\\Leftrightarrow & 6x+4& = &10-2-x \\\Leftrightarrow & 6x \color{red}{+4} & = &8 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 6x+x& = &8-4 \\\Leftrightarrow & 7x& = &4 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{4}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (6x-2)& = & -4 \color{red}{+} (-15+x) \\\Leftrightarrow & 30x-10& = &-4-15+x \\\Leftrightarrow & 30x \color{red}{-10} & = &-19 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 30x-x& = &-19+10 \\\Leftrightarrow & 29x& = &-9 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-9}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-9}{29} & & \\ & V = \left\{ \frac{-9}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-3x+1)& = & -4 \color{red}{+} (-10+x) \\\Leftrightarrow & -6x+2& = &-4-10+x \\\Leftrightarrow & -6x \color{red}{+2} & = &-14 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & -6x-x& = &-14-2 \\\Leftrightarrow & -7x& = &-16 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-16}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (2x-7)& = & 7 \color{red}{-} (-13+x) \\\Leftrightarrow & 12x-42& = &7+13-x \\\Leftrightarrow & 12x \color{red}{-42} & = &20 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 12x+x& = &20+42 \\\Leftrightarrow & 13x& = &62 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{62}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{62}{13} & & \\ & V = \left\{ \frac{62}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x+4)& = & -14 \color{red}{-} (4-5x) \\\Leftrightarrow & 8x+16& = &-14-4+5x \\\Leftrightarrow & 8x \color{red}{+16} & = &-18 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+16} \color{blue}{-16} \color{blue}{-5x} & = &-18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-16} \\\Leftrightarrow & 8x-5x& = &-18-16 \\\Leftrightarrow & 3x& = &-34 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-34}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-34}{3} & & \\ & V = \left\{ \frac{-34}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-5x-3)& = & -8 \color{red}{-} (-14+x) \\\Leftrightarrow & -20x-12& = &-8+14-x \\\Leftrightarrow & -20x \color{red}{-12} & = &6 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -20x+x& = &6+12 \\\Leftrightarrow & -19x& = &18 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{18}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-18}{19} & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-5x+7)& = & 5 \color{red}{-} (-1+2x) \\\Leftrightarrow & -25x+35& = &5+1-2x \\\Leftrightarrow & -25x \color{red}{+35} & = &6 \color{red}{-2x} \\\Leftrightarrow & -25x \color{red}{+35} \color{blue}{-35} \color{blue}{+2x} & = &6 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-35} \\\Leftrightarrow & -25x+2x& = &6-35 \\\Leftrightarrow & -23x& = &-29 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-29}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{29}{23} & & \\ & V = \left\{ \frac{29}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-6x+4)& = & 7 \color{red}{-} (4+x) \\\Leftrightarrow & -12x+8& = &7-4-x \\\Leftrightarrow & -12x \color{red}{+8} & = &3 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &3-8 \\\Leftrightarrow & -11x& = &-5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-4x-1)& = & 6 \color{red}{-} (-9+x) \\\Leftrightarrow & -12x-3& = &6+9-x \\\Leftrightarrow & -12x \color{red}{-3} & = &15 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -12x+x& = &15+3 \\\Leftrightarrow & -11x& = &18 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{18}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-18}{11} & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-3x-7)& = & 7 \color{red}{+} (12+x) \\\Leftrightarrow & -12x-28& = &7+12+x \\\Leftrightarrow & -12x \color{red}{-28} & = &19 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -12x-x& = &19+28 \\\Leftrightarrow & -13x& = &47 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{47}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-47}{13} & & \\ & V = \left\{ \frac{-47}{13} \right\} & \\\end{align}\)