Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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