Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-x } & = & 3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 3 \color{blue}{+6} \\\Leftrightarrow &-16x & = &9\\\Leftrightarrow & \color{red}{-16}x & = &9\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{9}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{16} } & & \\ & V = \left\{ \frac{-9}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+13}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13-x } & = & 8 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 8 \color{blue}{-13} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-7}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-7}\color{blue}{+7-x } & = & -11 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -11 \color{blue}{+7} \\\Leftrightarrow &-10x & = &-4\\\Leftrightarrow & \color{red}{-10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+1}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+1}\color{blue}{-1-13x } & = & 14 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 14 \color{blue}{-1} \\\Leftrightarrow &-10x & = &13\\\Leftrightarrow & \color{red}{-10}x & = &13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+14}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-13x } & = & 3 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &-25x & = &-11\\\Leftrightarrow & \color{red}{-25}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-11}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{11}{25} } & & \\ & V = \left\{ \frac{11}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-15}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-14x } & = & -7 \color{red}{ +14x }\color{blue}{+15-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &-23x & = &8\\\Leftrightarrow & \color{red}{-23}x & = &8\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{8}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{23} } & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-9}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9-7x } & = & -2 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &8x & = &7\\\Leftrightarrow & \color{red}{8}x & = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+9}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-x } & = & 5 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 5 \color{blue}{-9} \\\Leftrightarrow &-11x & = &-4\\\Leftrightarrow & \color{red}{-11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+11}& = & -1 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11+7x } & = & -1 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &19x & = &-12\\\Leftrightarrow & \color{red}{19}x & = &-12\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-12}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{19} } & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+13}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{+13}\color{blue}{-13-11x } & = & -13 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & 7x \color{blue}{-11x } & = & -13 \color{blue}{-13} \\\Leftrightarrow &-4x & = &-26\\\Leftrightarrow & \color{red}{-4}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-26}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{2} } & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-11}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-x } & = & 1 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 1 \color{blue}{+11} \\\Leftrightarrow &-16x & = &12\\\Leftrightarrow & \color{red}{-16}x & = &12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+15}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15+13x } & = & -11 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &27x & = &-26\\\Leftrightarrow & \color{red}{27}x & = &-26\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-26}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{27} } & & \\ & V = \left\{ \frac{-26}{27} \right\} & \\\end{align}\)