Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-2x-5)& = & 3 \color{red}{-} (2+3x) \\\Leftrightarrow & -8x-20& = &3-2-3x \\\Leftrightarrow & -8x \color{red}{-20} & = &1 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & -8x+3x& = &1+20 \\\Leftrightarrow & -5x& = &21 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{21}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-21}{5} & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x+5)& = & 1 \color{red}{+} (-13+3x) \\\Leftrightarrow & -4x+20& = &1-13+3x \\\Leftrightarrow & -4x \color{red}{+20} & = &-12 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &-12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & -4x-3x& = &-12-20 \\\Leftrightarrow & -7x& = &-32 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-32}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{32}{7} & & \\ & V = \left\{ \frac{32}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x-5)& = & 7 \color{red}{-} (-3+x) \\\Leftrightarrow & -12x-20& = &7+3-x \\\Leftrightarrow & -12x \color{red}{-20} & = &10 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -12x+x& = &10+20 \\\Leftrightarrow & -11x& = &30 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{30}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-30}{11} & & \\ & V = \left\{ \frac{-30}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (6x+5)& = & -15 \color{red}{+} (9-5x) \\\Leftrightarrow & 18x+15& = &-15+9-5x \\\Leftrightarrow & 18x \color{red}{+15} & = &-6 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+15} \color{blue}{-15} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-15} \\\Leftrightarrow & 18x+5x& = &-6-15 \\\Leftrightarrow & 23x& = &-21 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-21}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-21}{23} & & \\ & V = \left\{ \frac{-21}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-6x-2)& = & 11 \color{red}{-} (-13-5x) \\\Leftrightarrow & -36x-12& = &11+13+5x \\\Leftrightarrow & -36x \color{red}{-12} & = &24 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &24 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -36x-5x& = &24+12 \\\Leftrightarrow & -41x& = &36 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{36}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-36}{41} & & \\ & V = \left\{ \frac{-36}{41} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-4x-4)& = & -1 \color{red}{-} (7+x) \\\Leftrightarrow & -12x-12& = &-1-7-x \\\Leftrightarrow & -12x \color{red}{-12} & = &-8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &-8+12 \\\Leftrightarrow & -11x& = &4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (3x+4)& = & 8 \color{red}{+} (15-2x) \\\Leftrightarrow & 15x+20& = &8+15-2x \\\Leftrightarrow & 15x \color{red}{+20} & = &23 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &23 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & 15x+2x& = &23-20 \\\Leftrightarrow & 17x& = &3 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{3}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{3}{17} & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-4x+3)& = & -5 \color{red}{-} (9+x) \\\Leftrightarrow & -12x+9& = &-5-9-x \\\Leftrightarrow & -12x \color{red}{+9} & = &-14 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & -12x+x& = &-14-9 \\\Leftrightarrow & -11x& = &-23 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-23}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{23}{11} & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-2x-3)& = & -1 \color{red}{+} (-15+x) \\\Leftrightarrow & -8x-12& = &-1-15+x \\\Leftrightarrow & -8x \color{red}{-12} & = &-16 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -8x-x& = &-16+12 \\\Leftrightarrow & -9x& = &-4 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-4}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{4}{9} & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-6x-1)& = & -12 \color{red}{+} (-14+x) \\\Leftrightarrow & -12x-2& = &-12-14+x \\\Leftrightarrow & -12x \color{red}{-2} & = &-26 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-26 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -12x-x& = &-26+2 \\\Leftrightarrow & -13x& = &-24 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-24}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (x-6)& = & 5 \color{red}{-} (-10+4x) \\\Leftrightarrow & 5x-30& = &5+10-4x \\\Leftrightarrow & 5x \color{red}{-30} & = &15 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-30} \color{blue}{+30} \color{blue}{+4x} & = &15 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+30} \\\Leftrightarrow & 5x+4x& = &15+30 \\\Leftrightarrow & 9x& = &45 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{45}{ \color{red}{9} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-5x+3)& = & -6 \color{red}{-} (-15-4x) \\\Leftrightarrow & -25x+15& = &-6+15+4x \\\Leftrightarrow & -25x \color{red}{+15} & = &9 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &9 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & -25x-4x& = &9-15 \\\Leftrightarrow & -29x& = &-6 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-6}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{6}{29} & & \\ & V = \left\{ \frac{6}{29} \right\} & \\\end{align}\)