Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-7}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7-x } & = & 15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &13x & = &22\\\Leftrightarrow & \color{red}{13}x & = &22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+5}& = & 10 \color{red}{ +2x } \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5-2x } & = & 10 \color{red}{ +2x }\color{blue}{-5-2x } \\\Leftrightarrow & 3x \color{blue}{-2x } & = & 10 \color{blue}{-5} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-3}& = & 14 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-8x } & = & 14 \color{red}{ +8x }\color{blue}{+3-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &-13x & = &17\\\Leftrightarrow & \color{red}{-13}x & = &17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-4}& = & -10 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4-4x } & = & -10 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & -10 \color{blue}{+4} \\\Leftrightarrow &9x & = &-6\\\Leftrightarrow & \color{red}{9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-8}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8+11x } & = & -13 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &17x & = &-5\\\Leftrightarrow & \color{red}{17}x & = &-5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{17} } & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-x } & = & -10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -10 \color{blue}{-3} \\\Leftrightarrow &-4x & = &-13\\\Leftrightarrow & \color{red}{-4}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+11}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11-11x } & = & -2 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 3x \color{blue}{-11x } & = & -2 \color{blue}{-11} \\\Leftrightarrow &-8x & = &-13\\\Leftrightarrow & \color{red}{-8}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{8} } & & \\ & V = \left\{ \frac{13}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+14}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14+7x } & = & -13 \color{red}{ -7x }\color{blue}{-14+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &12x & = &-27\\\Leftrightarrow & \color{red}{12}x & = &-27\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-27}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-13}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-13}\color{blue}{+13-x } & = & 5 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{+13} \\\Leftrightarrow &-6x & = &18\\\Leftrightarrow & \color{red}{-6}x & = &18\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{18}{-6} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+7}& = & -3 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7+5x } & = & -3 \color{red}{ -5x }\color{blue}{-7+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -3 \color{blue}{-7} \\\Leftrightarrow &11x & = &-10\\\Leftrightarrow & \color{red}{11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-2}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-x } & = & 8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &-16x & = &10\\\Leftrightarrow & \color{red}{-16}x & = &10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-6}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-9x } & = & -14 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & -14 \color{blue}{+6} \\\Leftrightarrow &-7x & = &-8\\\Leftrightarrow & \color{red}{-7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)