Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (x-4)& = & -8 \color{red}{-} (7+x) \\\Leftrightarrow & 2x-8& = &-8-7-x \\\Leftrightarrow & 2x \color{red}{-8} & = &-15 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 2x+x& = &-15+8 \\\Leftrightarrow & 3x& = &-7 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-7}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x-3)& = & 14 \color{red}{-} (-4+x) \\\Leftrightarrow & 12x-12& = &14+4-x \\\Leftrightarrow & 12x \color{red}{-12} & = &18 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &18+12 \\\Leftrightarrow & 13x& = &30 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{30}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{30}{13} & & \\ & V = \left\{ \frac{30}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-3x-6)& = & -8 \color{red}{+} (3-2x) \\\Leftrightarrow & -15x-30& = &-8+3-2x \\\Leftrightarrow & -15x \color{red}{-30} & = &-5 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-30} \color{blue}{+30} \color{blue}{+2x} & = &-5 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+30} \\\Leftrightarrow & -15x+2x& = &-5+30 \\\Leftrightarrow & -13x& = &25 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{25}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-25}{13} & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-5x+3)& = & 2 \color{red}{+} (12-2x) \\\Leftrightarrow & -15x+9& = &2+12-2x \\\Leftrightarrow & -15x \color{red}{+9} & = &14 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+9} \color{blue}{-9} \color{blue}{+2x} & = &14 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-9} \\\Leftrightarrow & -15x+2x& = &14-9 \\\Leftrightarrow & -13x& = &5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x+3)& = & 9 \color{red}{-} (3+x) \\\Leftrightarrow & -24x+12& = &9-3-x \\\Leftrightarrow & -24x \color{red}{+12} & = &6 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -24x+x& = &6-12 \\\Leftrightarrow & -23x& = &-6 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-6}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{6}{23} & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-4x-4)& = & -11 \color{red}{+} (7+x) \\\Leftrightarrow & -12x-12& = &-11+7+x \\\Leftrightarrow & -12x \color{red}{-12} & = &-4 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &-4+12 \\\Leftrightarrow & -13x& = &8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (3x-4)& = & 2 \color{red}{-} (3+x) \\\Leftrightarrow & 12x-16& = &2-3-x \\\Leftrightarrow & 12x \color{red}{-16} & = &-1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 12x+x& = &-1+16 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (5x+7)& = & 5 \color{red}{-} (8+x) \\\Leftrightarrow & 10x+14& = &5-8-x \\\Leftrightarrow & 10x \color{red}{+14} & = &-3 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 10x+x& = &-3-14 \\\Leftrightarrow & 11x& = &-17 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-17}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-17}{11} & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x-1)& = & -2 \color{red}{-} (-7-4x) \\\Leftrightarrow & 9x-3& = &-2+7+4x \\\Leftrightarrow & 9x \color{red}{-3} & = &5 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-3} \color{blue}{+3} \color{blue}{-4x} & = &5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+3} \\\Leftrightarrow & 9x-4x& = &5+3 \\\Leftrightarrow & 5x& = &8 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{8}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{8}{5} & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (4x-6)& = & 9 \color{red}{-} (12+x) \\\Leftrightarrow & 20x-30& = &9-12-x \\\Leftrightarrow & 20x \color{red}{-30} & = &-3 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 20x+x& = &-3+30 \\\Leftrightarrow & 21x& = &27 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{27}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{9}{7} & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (2x-3)& = & 10 \color{red}{+} (8+x) \\\Leftrightarrow & 12x-18& = &10+8+x \\\Leftrightarrow & 12x \color{red}{-18} & = &18 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 12x-x& = &18+18 \\\Leftrightarrow & 11x& = &36 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{36}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{36}{11} & & \\ & V = \left\{ \frac{36}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-5x-3)& = & 7 \color{red}{+} (15+x) \\\Leftrightarrow & -20x-12& = &7+15+x \\\Leftrightarrow & -20x \color{red}{-12} & = &22 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -20x-x& = &22+12 \\\Leftrightarrow & -21x& = &34 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{34}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-34}{21} & & \\ & V = \left\{ \frac{-34}{21} \right\} & \\\end{align}\)