Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+15}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15-13x } & = & -13 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &-x & = &-28\\\Leftrightarrow & \color{red}{-}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-28}{-1} \\\Leftrightarrow & \color{green}{ x = 28 } & & \\ & V = \left\{ 28 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+10}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-13x } & = & -13 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &-28x & = &-23\\\Leftrightarrow & \color{red}{-28}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-23}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{23}{28} } & & \\ & V = \left\{ \frac{23}{28} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-x } & = & -11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &-6x & = &-24\\\Leftrightarrow & \color{red}{-6}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-24}{-6} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+12}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-x } & = & 6 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 6 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+8}& = & 5 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{+8}\color{blue}{-8+7x } & = & 5 \color{red}{ -7x }\color{blue}{-8+7x } \\\Leftrightarrow & x \color{blue}{+7x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &8x & = &-3\\\Leftrightarrow & \color{red}{8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-2}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2-5x } & = & 13 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 13 \color{blue}{+2} \\\Leftrightarrow &-7x & = &15\\\Leftrightarrow & \color{red}{-7}x & = &15\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{15}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-2}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-2}\color{blue}{+2-x } & = & -12 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -12 \color{blue}{+2} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-1}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-x } & = & -13 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -13 \color{blue}{+1} \\\Leftrightarrow &-16x & = &-12\\\Leftrightarrow & \color{red}{-16}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+1}& = & -13 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-14x } & = & -13 \color{red}{ +14x }\color{blue}{-1-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -13 \color{blue}{-1} \\\Leftrightarrow &-23x & = &-14\\\Leftrightarrow & \color{red}{-23}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-14}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{14}{23} } & & \\ & V = \left\{ \frac{14}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-8}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8-7x } & = & -14 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &5x & = &-6\\\Leftrightarrow & \color{red}{5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+11}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11-11x } & = & 7 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &x & = &-4\\\Leftrightarrow & \color{red}{}x & = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+13}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13+13x } & = & -14 \color{red}{ -13x }\color{blue}{-13+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -14 \color{blue}{-13} \\\Leftrightarrow &22x & = &-27\\\Leftrightarrow & \color{red}{22}x & = &-27\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-27}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{22} } & & \\ & V = \left\{ \frac{-27}{22} \right\} & \\\end{align}\)