Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(15x+4=-6+14x\)
2. \(10x+4=-10-3x\)
3. \(11x+8=6+5x\)
4. \(15x-7=-4+11x\)
5. \(-6x-5=-15+13x\)
6. \(-x+6=2+0x\)
7. \(5x-9=12+x\)
8. \(-6x-9=-13+7x\)
9. \(-13x+15=-7+x\)
10. \(11x+9=-1+8x\)
11. \(2x-12=-2+3x\)
12. \(15x+14=14+x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+4}& = & -6 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4-14x } & = & -6 \color{red}{ +14x }\color{blue}{-4-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+4}& = & -10 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+4}\color{blue}{-4+3x } & = & -10 \color{red}{ -3x }\color{blue}{-4+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &13x & = &-14\\\Leftrightarrow & \color{red}{13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+8}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8-5x } & = & 6 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & 6 \color{blue}{-8} \\\Leftrightarrow &6x & = &-2\\\Leftrightarrow & \color{red}{6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-2}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-7}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7-11x } & = & -4 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -4 \color{blue}{+7} \\\Leftrightarrow &4x & = &3\\\Leftrightarrow & \color{red}{4}x & = &3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-5}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-13x } & = & -15 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -15 \color{blue}{+5} \\\Leftrightarrow &-19x & = &-10\\\Leftrightarrow & \color{red}{-19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-10}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+6}& = & 2 \color{red}{ +0x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6+0x } & = & 2 \color{red}{ +0x }\color{blue}{-6+0x } \\\Leftrightarrow & -x \color{blue}{+0x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &-x & = &-4\\\Leftrightarrow & \color{red}{-}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-4}{-1} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-9}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9-x } & = & 12 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &4x & = &21\\\Leftrightarrow & \color{red}{4}x & = &21\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{21}{4} \\\Leftrightarrow & \color{green}{ x = \frac{21}{4} } & & \\ & V = \left\{ \frac{21}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-9}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-7x } & = & -13 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &-13x & = &-4\\\Leftrightarrow & \color{red}{-13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+15}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-x } & = & -7 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &-14x & = &-22\\\Leftrightarrow & \color{red}{-14}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-22}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+9}& = & -1 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9-8x } & = & -1 \color{red}{ +8x }\color{blue}{-9-8x } \\\Leftrightarrow & 11x \color{blue}{-8x } & = & -1 \color{blue}{-9} \\\Leftrightarrow &3x & = &-10\\\Leftrightarrow & \color{red}{3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-12}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12-3x } & = & -2 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &-x & = &10\\\Leftrightarrow & \color{red}{-}x & = &10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{10}{-1} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14-x } & = & 14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &14x & = &0\\\Leftrightarrow & \color{red}{14}x & = &0\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{0}{14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)