Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & -9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-15x & = &-14\\\Leftrightarrow & \color{red}{-15}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-4}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4-5x } & = & 14 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & 3x \color{blue}{-5x } & = & 14 \color{blue}{+4} \\\Leftrightarrow &-2x & = &18\\\Leftrightarrow & \color{red}{-2}x & = &18\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{18}{-2} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-x } & = & -11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+9}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-13x } & = & 4 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 4 \color{blue}{-9} \\\Leftrightarrow &-19x & = &-5\\\Leftrightarrow & \color{red}{-19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-7}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-x } & = & 15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &-4x & = &22\\\Leftrightarrow & \color{red}{-4}x & = &22\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{22}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6-x } & = & 9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &4x & = &3\\\Leftrightarrow & \color{red}{4}x & = &3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+6}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6-11x } & = & -12 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 7x \color{blue}{-11x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &-4x & = &-18\\\Leftrightarrow & \color{red}{-4}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-18}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+8}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-x } & = & -9 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -9 \color{blue}{-8} \\\Leftrightarrow &-9x & = &-17\\\Leftrightarrow & \color{red}{-9}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-17}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-7}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7+11x } & = & 10 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &17x & = &17\\\Leftrightarrow & \color{red}{17}x & = &17\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{17}{17} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-10}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-x } & = & -6 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -6 \color{blue}{+10} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-1}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1-x } & = & -3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -3 \color{blue}{+1} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+1}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-5x } & = & -2 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)