Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-2x+4)& = & -15 \color{red}{+} (2+x) \\\Leftrightarrow & -4x+8& = &-15+2+x \\\Leftrightarrow & -4x \color{red}{+8} & = &-13 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -4x-x& = &-13-8 \\\Leftrightarrow & -5x& = &-21 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-21}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{21}{5} & & \\ & V = \left\{ \frac{21}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x-6)& = & 3 \color{red}{-} (6+x) \\\Leftrightarrow & 10x-12& = &3-6-x \\\Leftrightarrow & 10x \color{red}{-12} & = &-3 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 10x+x& = &-3+12 \\\Leftrightarrow & 11x& = &9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-6x+5)& = & -5 \color{red}{-} (-1+x) \\\Leftrightarrow & -30x+25& = &-5+1-x \\\Leftrightarrow & -30x \color{red}{+25} & = &-4 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & -30x+x& = &-4-25 \\\Leftrightarrow & -29x& = &-29 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-29}{ \color{red}{-29} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-3x-3)& = & -7 \color{red}{-} (3-2x) \\\Leftrightarrow & -15x-15& = &-7-3+2x \\\Leftrightarrow & -15x \color{red}{-15} & = &-10 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &-10 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & -15x-2x& = &-10+15 \\\Leftrightarrow & -17x& = &5 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{5}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-5}{17} & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x-2)& = & -13 \color{red}{-} (-12+x) \\\Leftrightarrow & -24x-12& = &-13+12-x \\\Leftrightarrow & -24x \color{red}{-12} & = &-1 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -24x+x& = &-1+12 \\\Leftrightarrow & -23x& = &11 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{11}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-11}{23} & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x+1)& = & -11 \color{red}{+} (-10+x) \\\Leftrightarrow & 8x+4& = &-11-10+x \\\Leftrightarrow & 8x \color{red}{+4} & = &-21 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 8x-x& = &-21-4 \\\Leftrightarrow & 7x& = &-25 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-25}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (6x+5)& = & -4 \color{red}{+} (6-5x) \\\Leftrightarrow & 36x+30& = &-4+6-5x \\\Leftrightarrow & 36x \color{red}{+30} & = &2 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+30} \color{blue}{-30} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-30} \\\Leftrightarrow & 36x+5x& = &2-30 \\\Leftrightarrow & 41x& = &-28 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-28}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{-28}{41} & & \\ & V = \left\{ \frac{-28}{41} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (3x-4)& = & -12 \color{red}{+} (9+x) \\\Leftrightarrow & 12x-16& = &-12+9+x \\\Leftrightarrow & 12x \color{red}{-16} & = &-3 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 12x-x& = &-3+16 \\\Leftrightarrow & 11x& = &13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-6x+2)& = & 5 \color{red}{+} (5+x) \\\Leftrightarrow & -24x+8& = &5+5+x \\\Leftrightarrow & -24x \color{red}{+8} & = &10 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -24x-x& = &10-8 \\\Leftrightarrow & -25x& = &2 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{2}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-2}{25} & & \\ & V = \left\{ \frac{-2}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (3x+1)& = & 7 \color{red}{-} (13+x) \\\Leftrightarrow & 12x+4& = &7-13-x \\\Leftrightarrow & 12x \color{red}{+4} & = &-6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 12x+x& = &-6-4 \\\Leftrightarrow & 13x& = &-10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-4x-6)& = & 7 \color{red}{+} (-14+x) \\\Leftrightarrow & -8x-12& = &7-14+x \\\Leftrightarrow & -8x \color{red}{-12} & = &-7 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -8x-x& = &-7+12 \\\Leftrightarrow & -9x& = &5 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{5}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-5}{9} & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (3x-3)& = & -5 \color{red}{-} (1+x) \\\Leftrightarrow & 9x-9& = &-5-1-x \\\Leftrightarrow & 9x \color{red}{-9} & = &-6 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 9x+x& = &-6+9 \\\Leftrightarrow & 10x& = &3 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{3}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)