Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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