Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+8}& = & -4 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8+3x } & = & -4 \color{red}{ -3x }\color{blue}{-8+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -4 \color{blue}{-8} \\\Leftrightarrow &10x & = &-12\\\Leftrightarrow & \color{red}{10}x & = &-12\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-12}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{-1}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1-9x } & = & 13 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & 13x \color{blue}{-9x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &4x & = &14\\\Leftrightarrow & \color{red}{4}x & = &14\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{14}{4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+3}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+3}\color{blue}{-3-13x } & = & 1 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 1 \color{blue}{-3} \\\Leftrightarrow &-28x & = &-2\\\Leftrightarrow & \color{red}{-28}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-2}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-4}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-4}\color{blue}{+4-x } & = & -5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &-14x & = &-1\\\Leftrightarrow & \color{red}{-14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-6}& = & -3 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6+3x } & = & -3 \color{red}{ -3x }\color{blue}{+6+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &13x & = &3\\\Leftrightarrow & \color{red}{13}x & = &3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-11}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-x } & = & -6 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -6 \color{blue}{+11} \\\Leftrightarrow &-12x & = &5\\\Leftrightarrow & \color{red}{-12}x & = &5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{-1}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1+11x } & = & 15 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &17x & = &16\\\Leftrightarrow & \color{red}{17}x & = &16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+7}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7-3x } & = & -5 \color{red}{ +3x }\color{blue}{-7-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & -5 \color{blue}{-7} \\\Leftrightarrow &5x & = &-12\\\Leftrightarrow & \color{red}{5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-2}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2+11x } & = & 6 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &20x & = &8\\\Leftrightarrow & \color{red}{20}x & = &8\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{8}{20} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+8}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-9x } & = & 5 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &-17x & = &-3\\\Leftrightarrow & \color{red}{-17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9-x } & = & -13 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &14x & = &-22\\\Leftrightarrow & \color{red}{14}x & = &-22\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-22}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+9}& = & -4 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9-12x } & = & -4 \color{red}{ +12x }\color{blue}{-9-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & -4 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-13\\\Leftrightarrow & \color{red}{-5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)