Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+4}& = & -9 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4+9x } & = & -9 \color{red}{ -9x }\color{blue}{-4+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -9 \color{blue}{-4} \\\Leftrightarrow &23x & = &-13\\\Leftrightarrow & \color{red}{23}x & = &-13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{23} } & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-7}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-x } & = & -4 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -4 \color{blue}{+7} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-6}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-13x } & = & -12 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &-16x & = &-6\\\Leftrightarrow & \color{red}{-16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-14}& = & -14 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14-10x } & = & -14 \color{red}{ +10x }\color{blue}{+14-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & -14 \color{blue}{+14} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+5}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-x } & = & 8 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 8 \color{blue}{-5} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-15}& = & -6 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15+7x } & = & -6 \color{red}{ -7x }\color{blue}{+15+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &22x & = &9\\\Leftrightarrow & \color{red}{22}x & = &9\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{9}{22} \\\Leftrightarrow & \color{green}{ x = \frac{9}{22} } & & \\ & V = \left\{ \frac{9}{22} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+5}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-x } & = & -3 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-x } & = & 14 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &-14x & = &28\\\Leftrightarrow & \color{red}{-14}x & = &28\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{28}{-14} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-13}& = & -6 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13+14x } & = & -6 \color{red}{ -14x }\color{blue}{+13+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -6 \color{blue}{+13} \\\Leftrightarrow &19x & = &7\\\Leftrightarrow & \color{red}{19}x & = &7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+7}& = & 1 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7-14x } & = & 1 \color{red}{ +14x }\color{blue}{-7-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+1}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1-13x } & = & 1 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & 1 \color{blue}{-1} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+11}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-x } & = & -3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -3 \color{blue}{-11} \\\Leftrightarrow &-6x & = &-14\\\Leftrightarrow & \color{red}{-6}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)