Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-11}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11-11x } & = & -3 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 3x \color{blue}{-11x } & = & -3 \color{blue}{+11} \\\Leftrightarrow &-8x & = &8\\\Leftrightarrow & \color{red}{-8}x & = &8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{8}{-8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+14}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14-13x } & = & 5 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & 5 \color{blue}{-14} \\\Leftrightarrow &-2x & = &-9\\\Leftrightarrow & \color{red}{-2}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-9}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+12}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+12}\color{blue}{-12-x } & = & 2 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+15}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-7x } & = & -12 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &-20x & = &-27\\\Leftrightarrow & \color{red}{-20}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-27}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{27}{20} } & & \\ & V = \left\{ \frac{27}{20} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+2}& = & -2 \color{red}{ +2x } \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2-2x } & = & -2 \color{red}{ +2x }\color{blue}{-2-2x } \\\Leftrightarrow & 3x \color{blue}{-2x } & = & -2 \color{blue}{-2} \\\Leftrightarrow &x & = &-4\\\Leftrightarrow & \color{red}{}x & = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+9}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9-x } & = & -11 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -11 \color{blue}{-9} \\\Leftrightarrow &-15x & = &-20\\\Leftrightarrow & \color{red}{-15}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+2}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-5x } & = & 10 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 10 \color{blue}{-2} \\\Leftrightarrow &-3x & = &8\\\Leftrightarrow & \color{red}{-3}x & = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+13}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+13}\color{blue}{-13-5x } & = & 2 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 2 \color{blue}{-13} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+10}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-x } & = & 7 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-7}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-x } & = & -3 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+14}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14-7x } & = & -6 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &8x & = &-20\\\Leftrightarrow & \color{red}{8}x & = &-20\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-20}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+12}& = & -6 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12+13x } & = & -6 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -6 \color{blue}{-12} \\\Leftrightarrow &24x & = &-18\\\Leftrightarrow & \color{red}{24}x & = &-18\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-18}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)