Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-3x+5)& = & 5 \color{red}{-} (-4-5x) \\\Leftrightarrow & -18x+30& = &5+4+5x \\\Leftrightarrow & -18x \color{red}{+30} & = &9 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+30} \color{blue}{-30} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-30} \\\Leftrightarrow & -18x-5x& = &9-30 \\\Leftrightarrow & -23x& = &-21 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-21}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{21}{23} & & \\ & V = \left\{ \frac{21}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (x-2)& = & 10 \color{red}{+} (9+x) \\\Leftrightarrow & 2x-4& = &10+9+x \\\Leftrightarrow & 2x \color{red}{-4} & = &19 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 2x-x& = &19+4 \\\Leftrightarrow & x& = &23 \\ & V = \left\{ 23 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (3x-6)& = & -12 \color{red}{-} (15+x) \\\Leftrightarrow & 18x-36& = &-12-15-x \\\Leftrightarrow & 18x \color{red}{-36} & = &-27 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-27 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 18x+x& = &-27+36 \\\Leftrightarrow & 19x& = &9 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{9}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{9}{19} & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-6x+4)& = & 5 \color{red}{-} (-5-5x) \\\Leftrightarrow & -36x+24& = &5+5+5x \\\Leftrightarrow & -36x \color{red}{+24} & = &10 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & -36x-5x& = &10-24 \\\Leftrightarrow & -41x& = &-14 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{-14}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{14}{41} & & \\ & V = \left\{ \frac{14}{41} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (4x-4)& = & 9 \color{red}{-} (-12+x) \\\Leftrightarrow & 12x-12& = &9+12-x \\\Leftrightarrow & 12x \color{red}{-12} & = &21 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &21+12 \\\Leftrightarrow & 13x& = &33 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{33}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{33}{13} & & \\ & V = \left\{ \frac{33}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (5x+7)& = & 15 \color{red}{-} (12-3x) \\\Leftrightarrow & 10x+14& = &15-12+3x \\\Leftrightarrow & 10x \color{red}{+14} & = &3 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & 10x-3x& = &3-14 \\\Leftrightarrow & 7x& = &-11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x+2)& = & -11 \color{red}{+} (-2+x) \\\Leftrightarrow & 3x+6& = &-11-2+x \\\Leftrightarrow & 3x \color{red}{+6} & = &-13 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 3x-x& = &-13-6 \\\Leftrightarrow & 2x& = &-19 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-19}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{-19}{2} & & \\ & V = \left\{ \frac{-19}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x-4)& = & 14 \color{red}{-} (2+x) \\\Leftrightarrow & 6x-24& = &14-2-x \\\Leftrightarrow & 6x \color{red}{-24} & = &12 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 6x+x& = &12+24 \\\Leftrightarrow & 7x& = &36 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{36}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{36}{7} & & \\ & V = \left\{ \frac{36}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-2x+4)& = & -3 \color{red}{-} (-7-5x) \\\Leftrightarrow & -6x+12& = &-3+7+5x \\\Leftrightarrow & -6x \color{red}{+12} & = &4 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -6x-5x& = &4-12 \\\Leftrightarrow & -11x& = &-8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-5x-3)& = & -12 \color{red}{-} (-4-2x) \\\Leftrightarrow & -25x-15& = &-12+4+2x \\\Leftrightarrow & -25x \color{red}{-15} & = &-8 \color{red}{+2x} \\\Leftrightarrow & -25x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &-8 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & -25x-2x& = &-8+15 \\\Leftrightarrow & -27x& = &7 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = &\frac{7}{ \color{red}{-27} } \\\Leftrightarrow & x = \frac{-7}{27} & & \\ & V = \left\{ \frac{-7}{27} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (5x+5)& = & -8 \color{red}{+} (-10-2x) \\\Leftrightarrow & 15x+15& = &-8-10-2x \\\Leftrightarrow & 15x \color{red}{+15} & = &-18 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &-18 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & 15x+2x& = &-18-15 \\\Leftrightarrow & 17x& = &-33 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-33}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-33}{17} & & \\ & V = \left\{ \frac{-33}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (6x-2)& = & 3 \color{red}{-} (4+x) \\\Leftrightarrow & 12x-4& = &3-4-x \\\Leftrightarrow & 12x \color{red}{-4} & = &-1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 12x+x& = &-1+4 \\\Leftrightarrow & 13x& = &3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)