Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-5}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5-11x } & = & 12 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &-x & = &17\\\Leftrightarrow & \color{red}{-}x & = &17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{17}{-1} \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+8}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8-9x } & = & 5 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & -14x \color{blue}{-9x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &-23x & = &-3\\\Leftrightarrow & \color{red}{-23}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-3}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{3}{23} } & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+12}& = & -15 \color{red}{ -5x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12+5x } & = & -15 \color{red}{ -5x }\color{blue}{-12+5x } \\\Leftrightarrow & -11x \color{blue}{+5x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &-6x & = &-27\\\Leftrightarrow & \color{red}{-6}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-27}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-5}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-5x } & = & 10 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 10 \color{blue}{+5} \\\Leftrightarrow &-3x & = &15\\\Leftrightarrow & \color{red}{-3}x & = &15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{15}{-3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+7}& = & 13 \color{red}{ -7x } \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7+7x } & = & 13 \color{red}{ -7x }\color{blue}{-7+7x } \\\Leftrightarrow & -12x \color{blue}{+7x } & = & 13 \color{blue}{-7} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+7}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7-13x } & = & 10 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 10 \color{blue}{-7} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+12}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12-11x } & = & 4 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 4 \color{blue}{-12} \\\Leftrightarrow &-7x & = &-8\\\Leftrightarrow & \color{red}{-7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-10}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10-9x } & = & 10 \color{red}{ +9x }\color{blue}{+10-9x } \\\Leftrightarrow & 5x \color{blue}{-9x } & = & 10 \color{blue}{+10} \\\Leftrightarrow &-4x & = &20\\\Leftrightarrow & \color{red}{-4}x & = &20\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{20}{-4} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+10}& = & 12 \color{red}{ +15x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10-15x } & = & 12 \color{red}{ +15x }\color{blue}{-10-15x } \\\Leftrightarrow & 7x \color{blue}{-15x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &-8x & = &2\\\Leftrightarrow & \color{red}{-8}x & = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-1}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-1}\color{blue}{+1-7x } & = & -7 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -7 \color{blue}{+1} \\\Leftrightarrow &3x & = &-6\\\Leftrightarrow & \color{red}{3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-6}{3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+4}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+4}\color{blue}{-4-9x } & = & 13 \color{red}{ +9x }\color{blue}{-4-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-8}& = & 6 \color{red}{ +4x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-4x } & = & 6 \color{red}{ +4x }\color{blue}{+8-4x } \\\Leftrightarrow & -13x \color{blue}{-4x } & = & 6 \color{blue}{+8} \\\Leftrightarrow &-17x & = &14\\\Leftrightarrow & \color{red}{-17}x & = &14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)