Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x+5)& = & 2 \color{red}{+} (6+x) \\\Leftrightarrow & -30x+30& = &2+6+x \\\Leftrightarrow & -30x \color{red}{+30} & = &8 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -30x-x& = &8-30 \\\Leftrightarrow & -31x& = &-22 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-22}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{22}{31} & & \\ & V = \left\{ \frac{22}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (x+4)& = & 4 \color{red}{-} (6-5x) \\\Leftrightarrow & 6x+24& = &4-6+5x \\\Leftrightarrow & 6x \color{red}{+24} & = &-2 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &-2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & 6x-5x& = &-2-24 \\\Leftrightarrow & x& = &-26 \\ & V = \left\{ -26 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-5x+4)& = & 14 \color{red}{+} (-7-2x) \\\Leftrightarrow & -15x+12& = &14-7-2x \\\Leftrightarrow & -15x \color{red}{+12} & = &7 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+12} \color{blue}{-12} \color{blue}{+2x} & = &7 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-12} \\\Leftrightarrow & -15x+2x& = &7-12 \\\Leftrightarrow & -13x& = &-5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x+3)& = & -14 \color{red}{+} (-11-5x) \\\Leftrightarrow & 6x+9& = &-14-11-5x \\\Leftrightarrow & 6x \color{red}{+9} & = &-25 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+9} \color{blue}{-9} \color{blue}{+5x} & = &-25 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-9} \\\Leftrightarrow & 6x+5x& = &-25-9 \\\Leftrightarrow & 11x& = &-34 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-34}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-34}{11} & & \\ & V = \left\{ \frac{-34}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x-6)& = & -11 \color{red}{-} (1-2x) \\\Leftrightarrow & -3x-18& = &-11-1+2x \\\Leftrightarrow & -3x \color{red}{-18} & = &-12 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-18} \color{blue}{+18} \color{blue}{-2x} & = &-12 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+18} \\\Leftrightarrow & -3x-2x& = &-12+18 \\\Leftrightarrow & -5x& = &6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-2x-2)& = & -2 \color{red}{-} (7+3x) \\\Leftrightarrow & -4x-4& = &-2-7-3x \\\Leftrightarrow & -4x \color{red}{-4} & = &-9 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &-9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -4x+3x& = &-9+4 \\\Leftrightarrow & -x& = &-5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-5}{ \color{red}{-1} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-5x+5)& = & 7 \color{red}{-} (-8+3x) \\\Leftrightarrow & -20x+20& = &7+8-3x \\\Leftrightarrow & -20x \color{red}{+20} & = &15 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &15 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & -20x+3x& = &15-20 \\\Leftrightarrow & -17x& = &-5 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-5}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{5}{17} & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-2x-7)& = & -13 \color{red}{-} (12+x) \\\Leftrightarrow & -12x-42& = &-13-12-x \\\Leftrightarrow & -12x \color{red}{-42} & = &-25 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -12x+x& = &-25+42 \\\Leftrightarrow & -11x& = &17 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{17}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-17}{11} & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-3x-7)& = & 6 \color{red}{+} (-5-2x) \\\Leftrightarrow & -15x-35& = &6-5-2x \\\Leftrightarrow & -15x \color{red}{-35} & = &1 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-35} \color{blue}{+35} \color{blue}{+2x} & = &1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+35} \\\Leftrightarrow & -15x+2x& = &1+35 \\\Leftrightarrow & -13x& = &36 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{36}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-36}{13} & & \\ & V = \left\{ \frac{-36}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (5x-2)& = & -8 \color{red}{-} (12+x) \\\Leftrightarrow & 20x-8& = &-8-12-x \\\Leftrightarrow & 20x \color{red}{-8} & = &-20 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 20x+x& = &-20+8 \\\Leftrightarrow & 21x& = &-12 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-12}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-x-6)& = & -8 \color{red}{+} (-8-2x) \\\Leftrightarrow & -5x-30& = &-8-8-2x \\\Leftrightarrow & -5x \color{red}{-30} & = &-16 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{-30} \color{blue}{+30} \color{blue}{+2x} & = &-16 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+30} \\\Leftrightarrow & -5x+2x& = &-16+30 \\\Leftrightarrow & -3x& = &14 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{14}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-14}{3} & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (2x-2)& = & -2 \color{red}{+} (-9+x) \\\Leftrightarrow & 8x-8& = &-2-9+x \\\Leftrightarrow & 8x \color{red}{-8} & = &-11 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 8x-x& = &-11+8 \\\Leftrightarrow & 7x& = &-3 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-3}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)