Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-8}& = & 4 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8+7x } & = & 4 \color{red}{ -7x }\color{blue}{+8+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &22x & = &12\\\Leftrightarrow & \color{red}{22}x & = &12\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{12}{22} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-6}& = & -7 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6+14x } & = & -7 \color{red}{ -14x }\color{blue}{+6+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -7 \color{blue}{+6} \\\Leftrightarrow &19x & = &-1\\\Leftrightarrow & \color{red}{19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+13}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13-x } & = & 2 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 2 \color{blue}{-13} \\\Leftrightarrow &9x & = &-11\\\Leftrightarrow & \color{red}{9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+6}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6-13x } & = & 11 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 11 \color{blue}{-6} \\\Leftrightarrow &-10x & = &5\\\Leftrightarrow & \color{red}{-10}x & = &5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+10}& = & -4 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10-2x } & = & -4 \color{red}{ +2x }\color{blue}{-10-2x } \\\Leftrightarrow & 7x \color{blue}{-2x } & = & -4 \color{blue}{-10} \\\Leftrightarrow &5x & = &-14\\\Leftrightarrow & \color{red}{5}x & = &-14\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-14}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{5} } & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-2}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2-5x } & = & 3 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 3 \color{blue}{+2} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+9}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9+11x } & = & 15 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 15 \color{blue}{-9} \\\Leftrightarrow &23x & = &6\\\Leftrightarrow & \color{red}{23}x & = &6\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{6}{23} \\\Leftrightarrow & \color{green}{ x = \frac{6}{23} } & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-12}& = & -6 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+5x } & = & -6 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -6 \color{blue}{+12} \\\Leftrightarrow &8x & = &6\\\Leftrightarrow & \color{red}{8}x & = &6\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{6}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-12}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12-x } & = & -15 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-10}& = & 14 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10+7x } & = & 14 \color{red}{ -7x }\color{blue}{+10+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 14 \color{blue}{+10} \\\Leftrightarrow &19x & = &24\\\Leftrightarrow & \color{red}{19}x & = &24\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{24}{19} \\\Leftrightarrow & \color{green}{ x = \frac{24}{19} } & & \\ & V = \left\{ \frac{24}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+6}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-x } & = & -12 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &-7x & = &-18\\\Leftrightarrow & \color{red}{-7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+8}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8-9x } & = & 10 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &-20x & = &2\\\Leftrightarrow & \color{red}{-20}x & = &2\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{2}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)