Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+9}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-13x } & = & 1 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 1 \color{blue}{-9} \\\Leftrightarrow &-28x & = &-8\\\Leftrightarrow & \color{red}{-28}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-8}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-7}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7-3x } & = & 5 \color{red}{ +3x }\color{blue}{+7-3x } \\\Leftrightarrow & -x \color{blue}{-3x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &-4x & = &12\\\Leftrightarrow & \color{red}{-4}x & = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-7}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-13x } & = & 3 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 3 \color{blue}{+7} \\\Leftrightarrow &-25x & = &10\\\Leftrightarrow & \color{red}{-25}x & = &10\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{10}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-x } & = & -11 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &-10x & = &-26\\\Leftrightarrow & \color{red}{-10}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-26}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-10}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10-7x } & = & 13 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & 11x \color{blue}{-7x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &4x & = &23\\\Leftrightarrow & \color{red}{4}x & = &23\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{23}{4} \\\Leftrightarrow & \color{green}{ x = \frac{23}{4} } & & \\ & V = \left\{ \frac{23}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-15}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{-15}\color{blue}{+15-3x } & = & -2 \color{red}{ +3x }\color{blue}{+15-3x } \\\Leftrightarrow & 5x \color{blue}{-3x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &2x & = &13\\\Leftrightarrow & \color{red}{2}x & = &13\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{13}{2} \\\Leftrightarrow & \color{green}{ x = \frac{13}{2} } & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+9}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-x } & = & 3 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 3 \color{blue}{-9} \\\Leftrightarrow &-10x & = &-6\\\Leftrightarrow & \color{red}{-10}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-7}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-7x } & = & -2 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &-20x & = &5\\\Leftrightarrow & \color{red}{-20}x & = &5\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{5}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+5}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5-7x } & = & -13 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -13 \color{blue}{-5} \\\Leftrightarrow &-20x & = &-18\\\Leftrightarrow & \color{red}{-20}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-18}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-9}\color{blue}{+9-x } & = & -7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -7 \color{blue}{+9} \\\Leftrightarrow &-13x & = &2\\\Leftrightarrow & \color{red}{-13}x & = &2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-x } & = & 10 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 10 \color{blue}{-6} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-11}& = & 9 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11+7x } & = & 9 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & -x \color{blue}{+7x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &6x & = &20\\\Leftrightarrow & \color{red}{6}x & = &20\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{20}{6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)