Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-6}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6+13x } & = & -10 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -10 \color{blue}{+6} \\\Leftrightarrow &27x & = &-4\\\Leftrightarrow & \color{red}{27}x & = &-4\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-4}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{27} } & & \\ & V = \left\{ \frac{-4}{27} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-8}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8-x } & = & 3 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 3 \color{blue}{+8} \\\Leftrightarrow &5x & = &11\\\Leftrightarrow & \color{red}{5}x & = &11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12-x } & = & 10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &-10x & = &-2\\\Leftrightarrow & \color{red}{-10}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-15}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-5x } & = & 1 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 1 \color{blue}{+15} \\\Leftrightarrow &-9x & = &16\\\Leftrightarrow & \color{red}{-9}x & = &16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-11}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11-9x } & = & 5 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & x \color{blue}{-9x } & = & 5 \color{blue}{+11} \\\Leftrightarrow &-8x & = &16\\\Leftrightarrow & \color{red}{-8}x & = &16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{16}{-8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-15}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15-7x } & = & -7 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &3x & = &8\\\Leftrightarrow & \color{red}{3}x & = &8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+12}& = & 11 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12+13x } & = & 11 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &24x & = &-1\\\Leftrightarrow & \color{red}{24}x & = &-1\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-1}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{24} } & & \\ & V = \left\{ \frac{-1}{24} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+2}& = & -10 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2-4x } & = & -10 \color{red}{ +4x }\color{blue}{-2-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &-11x & = &-12\\\Leftrightarrow & \color{red}{-11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+11}& = & -11 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11+7x } & = & -11 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -11 \color{blue}{-11} \\\Leftrightarrow &19x & = &-22\\\Leftrightarrow & \color{red}{19}x & = &-22\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-22}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{19} } & & \\ & V = \left\{ \frac{-22}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-10}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10-13x } & = & -7 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-4x & = &3\\\Leftrightarrow & \color{red}{-4}x & = &3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+7}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-11x } & = & -3 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -3 \color{blue}{-7} \\\Leftrightarrow &-16x & = &-10\\\Leftrightarrow & \color{red}{-16}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+9}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+9}\color{blue}{-9-x } & = & -14 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -14 \color{blue}{-9} \\\Leftrightarrow &-3x & = &-23\\\Leftrightarrow & \color{red}{-3}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-23}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{23}{3} } & & \\ & V = \left\{ \frac{23}{3} \right\} & \\\end{align}\)