Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+3}& = & 7 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3+5x } & = & 7 \color{red}{ -5x }\color{blue}{-3+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+3}& = & 4 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3+2x } & = & 4 \color{red}{ -2x }\color{blue}{-3+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-x } & = & -4 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &-3x & = &8\\\Leftrightarrow & \color{red}{-3}x & = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+9}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9+13x } & = & 3 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 3 \color{blue}{-9} \\\Leftrightarrow &27x & = &-6\\\Leftrightarrow & \color{red}{27}x & = &-6\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-6}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+2}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2+5x } & = & 2 \color{red}{ -5x }\color{blue}{-2+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 2 \color{blue}{-2} \\\Leftrightarrow &8x & = &0\\\Leftrightarrow & \color{red}{8}x & = &0\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{0}{8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-5}& = & 2 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5-14x } & = & 2 \color{red}{ +14x }\color{blue}{+5-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+9}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-7x } & = & -11 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -11 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-20\\\Leftrightarrow & \color{red}{-16}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-20}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-6}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6-x } & = & 15 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &13x & = &21\\\Leftrightarrow & \color{red}{13}x & = &21\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{21}{13} \\\Leftrightarrow & \color{green}{ x = \frac{21}{13} } & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+7}& = & -15 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{+7}\color{blue}{-7-8x } & = & -15 \color{red}{ +8x }\color{blue}{-7-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & -15 \color{blue}{-7} \\\Leftrightarrow &-x & = &-22\\\Leftrightarrow & \color{red}{-}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-22}{-1} \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+2}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2-x } & = & -6 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &-16x & = &-8\\\Leftrightarrow & \color{red}{-16}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-x } & = & -2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &-16x & = &13\\\Leftrightarrow & \color{red}{-16}x & = &13\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{13}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{16} } & & \\ & V = \left\{ \frac{-13}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11-x } & = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &13x & = &14\\\Leftrightarrow & \color{red}{13}x & = &14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)