Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-2}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2-x } & = & -7 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -7 \color{blue}{+2} \\\Leftrightarrow &-4x & = &-5\\\Leftrightarrow & \color{red}{-4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-12}& = & 11 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12+13x } & = & 11 \color{red}{ -13x }\color{blue}{+12+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 11 \color{blue}{+12} \\\Leftrightarrow &20x & = &23\\\Leftrightarrow & \color{red}{20}x & = &23\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{23}{20} \\\Leftrightarrow & \color{green}{ x = \frac{23}{20} } & & \\ & V = \left\{ \frac{23}{20} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-5}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5-x } & = & -8 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -8 \color{blue}{+5} \\\Leftrightarrow &-16x & = &-3\\\Leftrightarrow & \color{red}{-16}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-x } & = & -8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &-8x & = &4\\\Leftrightarrow & \color{red}{-8}x & = &4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-1}& = & 14 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1+4x } & = & 14 \color{red}{ -4x }\color{blue}{+1+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 14 \color{blue}{+1} \\\Leftrightarrow &13x & = &15\\\Leftrightarrow & \color{red}{13}x & = &15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+1}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-5x } & = & 4 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 4 \color{blue}{-1} \\\Leftrightarrow &-17x & = &3\\\Leftrightarrow & \color{red}{-17}x & = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+15}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-7x } & = & -6 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -6 \color{blue}{-15} \\\Leftrightarrow &-16x & = &-21\\\Leftrightarrow & \color{red}{-16}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-21}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{21}{16} } & & \\ & V = \left\{ \frac{21}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+12}& = & -2 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-9x } & = & -2 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & -2 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-14\\\Leftrightarrow & \color{red}{-11}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{14}{11} } & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-15}& = & -3 \color{red}{ -15x } \\\Leftrightarrow & x \color{red}{-15}\color{blue}{+15+15x } & = & -3 \color{red}{ -15x }\color{blue}{+15+15x } \\\Leftrightarrow & x \color{blue}{+15x } & = & -3 \color{blue}{+15} \\\Leftrightarrow &16x & = &12\\\Leftrightarrow & \color{red}{16}x & = &12\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{12}{16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+11}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11-x } & = & -3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -3 \color{blue}{-11} \\\Leftrightarrow &10x & = &-14\\\Leftrightarrow & \color{red}{10}x & = &-14\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-14}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+7}& = & -10 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{+7}\color{blue}{-7-2x } & = & -10 \color{red}{ +2x }\color{blue}{-7-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & -10 \color{blue}{-7} \\\Leftrightarrow &9x & = &-17\\\Leftrightarrow & \color{red}{9}x & = &-17\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-17}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{9} } & & \\ & V = \left\{ \frac{-17}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-x } & = & 12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &-5x & = &17\\\Leftrightarrow & \color{red}{-5}x & = &17\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{17}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{5} } & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)