Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-5x-5)& = & 4 \color{red}{-} (6+x) \\\Leftrightarrow & -10x-10& = &4-6-x \\\Leftrightarrow & -10x \color{red}{-10} & = &-2 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -10x+x& = &-2+10 \\\Leftrightarrow & -9x& = &8 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{8}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-8}{9} & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x-4)& = & -15 \color{red}{+} (-6+3x) \\\Leftrightarrow & 25x-20& = &-15-6+3x \\\Leftrightarrow & 25x \color{red}{-20} & = &-21 \color{red}{+3x} \\\Leftrightarrow & 25x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &-21 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & 25x-3x& = &-21+20 \\\Leftrightarrow & 22x& = &-1 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = &\frac{-1}{ \color{red}{22} } \\\Leftrightarrow & x = \frac{-1}{22} & & \\ & V = \left\{ \frac{-1}{22} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-3x+3)& = & -11 \color{red}{+} (-8-4x) \\\Leftrightarrow & -9x+9& = &-11-8-4x \\\Leftrightarrow & -9x \color{red}{+9} & = &-19 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+9} \color{blue}{-9} \color{blue}{+4x} & = &-19 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-9} \\\Leftrightarrow & -9x+4x& = &-19-9 \\\Leftrightarrow & -5x& = &-28 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-28}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{28}{5} & & \\ & V = \left\{ \frac{28}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-2x-5)& = & 2 \color{red}{-} (-6-3x) \\\Leftrightarrow & -4x-10& = &2+6+3x \\\Leftrightarrow & -4x \color{red}{-10} & = &8 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -4x-3x& = &8+10 \\\Leftrightarrow & -7x& = &18 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{18}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-18}{7} & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-3x-2)& = & -10 \color{red}{+} (-2-5x) \\\Leftrightarrow & -18x-12& = &-10-2-5x \\\Leftrightarrow & -18x \color{red}{-12} & = &-12 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &-12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -18x+5x& = &-12+12 \\\Leftrightarrow & -13x& = &0 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{0}{ \color{red}{-13} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-2x-2)& = & 11 \color{red}{-} (-9+x) \\\Leftrightarrow & -10x-10& = &11+9-x \\\Leftrightarrow & -10x \color{red}{-10} & = &20 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -10x+x& = &20+10 \\\Leftrightarrow & -9x& = &30 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{30}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-10}{3} & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (3x-1)& = & -12 \color{red}{+} (4+x) \\\Leftrightarrow & 12x-4& = &-12+4+x \\\Leftrightarrow & 12x \color{red}{-4} & = &-8 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 12x-x& = &-8+4 \\\Leftrightarrow & 11x& = &-4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (x+4)& = & -15 \color{red}{+} (5+3x) \\\Leftrightarrow & 4x+16& = &-15+5+3x \\\Leftrightarrow & 4x \color{red}{+16} & = &-10 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & 4x-3x& = &-10-16 \\\Leftrightarrow & x& = &-26 \\ & V = \left\{ -26 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-4x+5)& = & 14 \color{red}{+} (-1+x) \\\Leftrightarrow & -16x+20& = &14-1+x \\\Leftrightarrow & -16x \color{red}{+20} & = &13 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -16x-x& = &13-20 \\\Leftrightarrow & -17x& = &-7 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-7}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{7}{17} & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-x-2)& = & 12 \color{red}{+} (-8+x) \\\Leftrightarrow & -4x-8& = &12-8+x \\\Leftrightarrow & -4x \color{red}{-8} & = &4 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -4x-x& = &4+8 \\\Leftrightarrow & -5x& = &12 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{12}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-12}{5} & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-x-1)& = & 4 \color{red}{+} (8+x) \\\Leftrightarrow & -6x-6& = &4+8+x \\\Leftrightarrow & -6x \color{red}{-6} & = &12 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -6x-x& = &12+6 \\\Leftrightarrow & -7x& = &18 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{18}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-18}{7} & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (6x-5)& = & 14 \color{red}{-} (14+x) \\\Leftrightarrow & 24x-20& = &14-14-x \\\Leftrightarrow & 24x \color{red}{-20} & = &0 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 24x+x& = &0+20 \\\Leftrightarrow & 25x& = &20 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{20}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)