Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-3x+3)& = & -6 \color{red}{-} (1+4x) \\\Leftrightarrow & -9x+9& = &-6-1-4x \\\Leftrightarrow & -9x \color{red}{+9} & = &-7 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+9} \color{blue}{-9} \color{blue}{+4x} & = &-7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-9} \\\Leftrightarrow & -9x+4x& = &-7-9 \\\Leftrightarrow & -5x& = &-16 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-16}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{16}{5} & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-6x-4)& = & 2 \color{red}{-} (-9+x) \\\Leftrightarrow & -24x-16& = &2+9-x \\\Leftrightarrow & -24x \color{red}{-16} & = &11 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -24x+x& = &11+16 \\\Leftrightarrow & -23x& = &27 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{27}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-27}{23} & & \\ & V = \left\{ \frac{-27}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-6x-6)& = & -5 \color{red}{+} (13+x) \\\Leftrightarrow & -12x-12& = &-5+13+x \\\Leftrightarrow & -12x \color{red}{-12} & = &8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &8+12 \\\Leftrightarrow & -13x& = &20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (5x+3)& = & 5 \color{red}{+} (7+3x) \\\Leftrightarrow & 10x+6& = &5+7+3x \\\Leftrightarrow & 10x \color{red}{+6} & = &12 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & 10x-3x& = &12-6 \\\Leftrightarrow & 7x& = &6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-x-2)& = & -10 \color{red}{-} (-10+x) \\\Leftrightarrow & -6x-12& = &-10+10-x \\\Leftrightarrow & -6x \color{red}{-12} & = &0 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -6x+x& = &0+12 \\\Leftrightarrow & -5x& = &12 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{12}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-12}{5} & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x+4)& = & 2 \color{red}{+} (8+x) \\\Leftrightarrow & 8x+16& = &2+8+x \\\Leftrightarrow & 8x \color{red}{+16} & = &10 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 8x-x& = &10-16 \\\Leftrightarrow & 7x& = &-6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (3x+6)& = & -13 \color{red}{+} (6-5x) \\\Leftrightarrow & 6x+12& = &-13+6-5x \\\Leftrightarrow & 6x \color{red}{+12} & = &-7 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 6x+5x& = &-7-12 \\\Leftrightarrow & 11x& = &-19 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-19}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-19}{11} & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-6x+5)& = & 4 \color{red}{+} (15+x) \\\Leftrightarrow & -36x+30& = &4+15+x \\\Leftrightarrow & -36x \color{red}{+30} & = &19 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -36x-x& = &19-30 \\\Leftrightarrow & -37x& = &-11 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-11}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{11}{37} & & \\ & V = \left\{ \frac{11}{37} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x+5)& = & 7 \color{red}{-} (10+x) \\\Leftrightarrow & 16x+20& = &7-10-x \\\Leftrightarrow & 16x \color{red}{+20} & = &-3 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 16x+x& = &-3-20 \\\Leftrightarrow & 17x& = &-23 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-23}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-23}{17} & & \\ & V = \left\{ \frac{-23}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (4x+2)& = & -6 \color{red}{-} (5+3x) \\\Leftrightarrow & 8x+4& = &-6-5-3x \\\Leftrightarrow & 8x \color{red}{+4} & = &-11 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 8x+3x& = &-11-4 \\\Leftrightarrow & 11x& = &-15 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-15}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-15}{11} & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x-3)& = & -5 \color{red}{+} (-14+x) \\\Leftrightarrow & -20x-12& = &-5-14+x \\\Leftrightarrow & -20x \color{red}{-12} & = &-19 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -20x-x& = &-19+12 \\\Leftrightarrow & -21x& = &-7 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-7}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{1}{3} & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-x-5)& = & -12 \color{red}{-} (10+x) \\\Leftrightarrow & -3x-15& = &-12-10-x \\\Leftrightarrow & -3x \color{red}{-15} & = &-22 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -3x+x& = &-22+15 \\\Leftrightarrow & -2x& = &-7 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-7}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{7}{2} & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)