Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+10}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10-x } & = & -12 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -12 \color{blue}{-10} \\\Leftrightarrow &2x & = &-22\\\Leftrightarrow & \color{red}{2}x & = &-22\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-22}{2} \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-4}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-x } & = & -1 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -1 \color{blue}{+4} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-8}& = & 7 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-8x } & = & 7 \color{red}{ +8x }\color{blue}{+8-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 7 \color{blue}{+8} \\\Leftrightarrow &-23x & = &15\\\Leftrightarrow & \color{red}{-23}x & = &15\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{15}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{23} } & & \\ & V = \left\{ \frac{-15}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-8}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8-x } & = & -4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &-12x & = &4\\\Leftrightarrow & \color{red}{-12}x & = &4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-12}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-5x } & = & 4 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 4 \color{blue}{+12} \\\Leftrightarrow &-17x & = &16\\\Leftrightarrow & \color{red}{-17}x & = &16\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{16}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-3}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3-13x } & = & 12 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 12 \color{blue}{+3} \\\Leftrightarrow &-3x & = &15\\\Leftrightarrow & \color{red}{-3}x & = &15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{15}{-3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-15}& = & 5 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-14x } & = & 5 \color{red}{ +14x }\color{blue}{+15-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 5 \color{blue}{+15} \\\Leftrightarrow &-27x & = &20\\\Leftrightarrow & \color{red}{-27}x & = &20\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{20}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{27} } & & \\ & V = \left\{ \frac{-20}{27} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+7}& = & -12 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7+15x } & = & -12 \color{red}{ -15x }\color{blue}{-7+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &23x & = &-19\\\Leftrightarrow & \color{red}{23}x & = &-19\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-19}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{23} } & & \\ & V = \left\{ \frac{-19}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{-6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6-x } & = & 7 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-10}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10-5x } & = & 2 \color{red}{ +5x }\color{blue}{+10-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &-6x & = &12\\\Leftrightarrow & \color{red}{-6}x & = &12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{12}{-6} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-9}& = & 1 \color{red}{ -14x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+14x } & = & 1 \color{red}{ -14x }\color{blue}{+9+14x } \\\Leftrightarrow & x \color{blue}{+14x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &15x & = &10\\\Leftrightarrow & \color{red}{15}x & = &10\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{10}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-x } & = & -7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-21\\\Leftrightarrow & \color{red}{-7}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-21}{-7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)