Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-6}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-6}\color{blue}{+6-11x } & = & 4 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 4 \color{blue}{+6} \\\Leftrightarrow &4x & = &10\\\Leftrightarrow & \color{red}{4}x & = &10\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{10}{4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+9}& = & -3 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9-8x } & = & -3 \color{red}{ +8x }\color{blue}{-9-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & -3 \color{blue}{-9} \\\Leftrightarrow &-7x & = &-12\\\Leftrightarrow & \color{red}{-7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-x } & = & -7 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &-4x & = &7\\\Leftrightarrow & \color{red}{-4}x & = &7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-9}& = & -8 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9-12x } & = & -8 \color{red}{ +12x }\color{blue}{+9-12x } \\\Leftrightarrow & 5x \color{blue}{-12x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+4}& = & -2 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4+13x } & = & -2 \color{red}{ -13x }\color{blue}{-4+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &27x & = &-6\\\Leftrightarrow & \color{red}{27}x & = &-6\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-6}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-14}\color{blue}{+14-x } & = & 4 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 4 \color{blue}{+14} \\\Leftrightarrow &-11x & = &18\\\Leftrightarrow & \color{red}{-11}x & = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+8}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8-x } & = & -4 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -4 \color{blue}{-8} \\\Leftrightarrow &-12x & = &-12\\\Leftrightarrow & \color{red}{-12}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-12}{-12} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3-x } & = & 13 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-10}& = & -14 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10+14x } & = & -14 \color{red}{ -14x }\color{blue}{+10+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -14 \color{blue}{+10} \\\Leftrightarrow &19x & = &-4\\\Leftrightarrow & \color{red}{19}x & = &-4\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-4}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-2}& = & -2 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2+12x } & = & -2 \color{red}{ -12x }\color{blue}{+2+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &17x & = &0\\\Leftrightarrow & \color{red}{17}x & = &0\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{0}{17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-10}& = & 7 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10+13x } & = & 7 \color{red}{ -13x }\color{blue}{+10+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &20x & = &17\\\Leftrightarrow & \color{red}{20}x & = &17\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{17}{20} \\\Leftrightarrow & \color{green}{ x = \frac{17}{20} } & & \\ & V = \left\{ \frac{17}{20} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-7}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-7}\color{blue}{+7-x } & = & -2 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)