Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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