Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+14}& = & -10 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14-8x } & = & -10 \color{red}{ +8x }\color{blue}{-14-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & -10 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-24\\\Leftrightarrow & \color{red}{-5}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-24}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{24}{5} } & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-13}& = & -7 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13-11x } & = & -7 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -7 \color{blue}{+13} \\\Leftrightarrow &-6x & = &6\\\Leftrightarrow & \color{red}{-6}x & = &6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{6}{-6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+3}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3-7x } & = & -11 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & -11 \color{blue}{-3} \\\Leftrightarrow &2x & = &-14\\\Leftrightarrow & \color{red}{2}x & = &-14\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-14}{2} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-10}& = & -7 \color{red}{ +8x } \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10-8x } & = & -7 \color{red}{ +8x }\color{blue}{+10-8x } \\\Leftrightarrow & -x \color{blue}{-8x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+14}\color{blue}{-14-x } & = & -7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &-15x & = &-21\\\Leftrightarrow & \color{red}{-15}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-21}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+5}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5-3x } & = & 4 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+6}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6-x } & = & -12 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &x & = &-18\\\Leftrightarrow & \color{red}{}x & = &-18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -18 \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-13}& = & -5 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13-8x } & = & -5 \color{red}{ +8x }\color{blue}{+13-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & -5 \color{blue}{+13} \\\Leftrightarrow &-7x & = &8\\\Leftrightarrow & \color{red}{-7}x & = &8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-3}& = & 12 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-3}\color{blue}{+3+14x } & = & 12 \color{red}{ -14x }\color{blue}{+3+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 12 \color{blue}{+3} \\\Leftrightarrow &29x & = &15\\\Leftrightarrow & \color{red}{29}x & = &15\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{15}{29} \\\Leftrightarrow & \color{green}{ x = \frac{15}{29} } & & \\ & V = \left\{ \frac{15}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+10}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+10}\color{blue}{-10-x } & = & 12 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-13}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13-9x } & = & -4 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -4 \color{blue}{+13} \\\Leftrightarrow &-13x & = &9\\\Leftrightarrow & \color{red}{-13}x & = &9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-8}& = & 9 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8+2x } & = & 9 \color{red}{ -2x }\color{blue}{+8+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 9 \color{blue}{+8} \\\Leftrightarrow &5x & = &17\\\Leftrightarrow & \color{red}{5}x & = &17\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{17}{5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)