Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-4}& = & 11 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4+9x } & = & 11 \color{red}{ -9x }\color{blue}{+4+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &23x & = &15\\\Leftrightarrow & \color{red}{23}x & = &15\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{15}{23} \\\Leftrightarrow & \color{green}{ x = \frac{15}{23} } & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-7}& = & 3 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7-15x } & = & 3 \color{red}{ +15x }\color{blue}{+7-15x } \\\Leftrightarrow & -x \color{blue}{-15x } & = & 3 \color{blue}{+7} \\\Leftrightarrow &-16x & = &10\\\Leftrightarrow & \color{red}{-16}x & = &10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-10}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-x } & = & 12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &x & = &22\\\Leftrightarrow & \color{red}{}x & = &22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 22 \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-13}& = & -14 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13+9x } & = & -14 \color{red}{ -9x }\color{blue}{+13+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & -14 \color{blue}{+13} \\\Leftrightarrow &8x & = &-1\\\Leftrightarrow & \color{red}{8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+3}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3-x } & = & -7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -7 \color{blue}{-3} \\\Leftrightarrow &-3x & = &-10\\\Leftrightarrow & \color{red}{-3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{+13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-x } & = & 4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &-8x & = &-9\\\Leftrightarrow & \color{red}{-8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-x } & = & 12 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 12 \color{blue}{-12} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-x } & = & -10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-10x & = &-1\\\Leftrightarrow & \color{red}{-10}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-9}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-13x } & = & -7 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -7 \color{blue}{+9} \\\Leftrightarrow &-19x & = &2\\\Leftrightarrow & \color{red}{-19}x & = &2\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{2}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-7}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-7}\color{blue}{+7-9x } & = & -5 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -5 \color{blue}{+7} \\\Leftrightarrow &-17x & = &2\\\Leftrightarrow & \color{red}{-17}x & = &2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-13}& = & 13 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13+8x } & = & 13 \color{red}{ -8x }\color{blue}{+13+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &11x & = &26\\\Leftrightarrow & \color{red}{11}x & = &26\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{26}{11} \\\Leftrightarrow & \color{green}{ x = \frac{26}{11} } & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2-x } & = & -3 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -3 \color{blue}{+2} \\\Leftrightarrow &9x & = &-1\\\Leftrightarrow & \color{red}{9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)