Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+10}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-x } & = & -6 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -6 \color{blue}{-10} \\\Leftrightarrow &-16x & = &-16\\\Leftrightarrow & \color{red}{-16}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-16}{-16} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{+7}& = & -14 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7-2x } & = & -14 \color{red}{ +2x }\color{blue}{-7-2x } \\\Leftrightarrow & 13x \color{blue}{-2x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &11x & = &-21\\\Leftrightarrow & \color{red}{11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-6}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-13x } & = & 7 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &-25x & = &13\\\Leftrightarrow & \color{red}{-25}x & = &13\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{13}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{25} } & & \\ & V = \left\{ \frac{-13}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+1}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1+11x } & = & 1 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 1 \color{blue}{-1} \\\Leftrightarrow &26x & = &0\\\Leftrightarrow & \color{red}{26}x & = &0\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{0}{26} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+5}& = & 2 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5-8x } & = & 2 \color{red}{ +8x }\color{blue}{-5-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & 2 \color{blue}{-5} \\\Leftrightarrow &-5x & = &-3\\\Leftrightarrow & \color{red}{-5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+7}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7-13x } & = & -15 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -15 \color{blue}{-7} \\\Leftrightarrow &-7x & = &-22\\\Leftrightarrow & \color{red}{-7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{22}{7} } & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+14}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-5x } & = & -12 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &-14x & = &-26\\\Leftrightarrow & \color{red}{-14}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-26}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+14}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-7x } & = & 13 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &-17x & = &-1\\\Leftrightarrow & \color{red}{-17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-6}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & -9 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -9 \color{blue}{+6} \\\Leftrightarrow &-4x & = &-3\\\Leftrightarrow & \color{red}{-4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-9}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9-x } & = & 12 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &3x & = &21\\\Leftrightarrow & \color{red}{3}x & = &21\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{21}{3} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+15}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-x } & = & -15 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -15 \color{blue}{-15} \\\Leftrightarrow &7x & = &-30\\\Leftrightarrow & \color{red}{7}x & = &-30\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-30}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-30}{7} } & & \\ & V = \left\{ \frac{-30}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-8}& = & -7 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8-11x } & = & -7 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -7 \color{blue}{+8} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)