Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (4x+5)& = & -15 \color{red}{+} (10+x) \\\Leftrightarrow & 12x+15& = &-15+10+x \\\Leftrightarrow & 12x \color{red}{+15} & = &-5 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 12x-x& = &-5-15 \\\Leftrightarrow & 11x& = &-20 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-20}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-20}{11} & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (4x+2)& = & 10 \color{red}{+} (12+x) \\\Leftrightarrow & 16x+8& = &10+12+x \\\Leftrightarrow & 16x \color{red}{+8} & = &22 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 16x-x& = &22-8 \\\Leftrightarrow & 15x& = &14 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{14}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{14}{15} & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-5x-6)& = & -15 \color{red}{+} (14-4x) \\\Leftrightarrow & -25x-30& = &-15+14-4x \\\Leftrightarrow & -25x \color{red}{-30} & = &-1 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-30} \color{blue}{+30} \color{blue}{+4x} & = &-1 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+30} \\\Leftrightarrow & -25x+4x& = &-1+30 \\\Leftrightarrow & -21x& = &29 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{29}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-29}{21} & & \\ & V = \left\{ \frac{-29}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-5x-2)& = & -2 \color{red}{+} (-14-4x) \\\Leftrightarrow & -25x-10& = &-2-14-4x \\\Leftrightarrow & -25x \color{red}{-10} & = &-16 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-10} \color{blue}{+10} \color{blue}{+4x} & = &-16 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+10} \\\Leftrightarrow & -25x+4x& = &-16+10 \\\Leftrightarrow & -21x& = &-6 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-6}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-2x-6)& = & 10 \color{red}{+} (4-3x) \\\Leftrightarrow & -10x-30& = &10+4-3x \\\Leftrightarrow & -10x \color{red}{-30} & = &14 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-30} \color{blue}{+30} \color{blue}{+3x} & = &14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+30} \\\Leftrightarrow & -10x+3x& = &14+30 \\\Leftrightarrow & -7x& = &44 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{44}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-44}{7} & & \\ & V = \left\{ \frac{-44}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-5x+2)& = & -2 \color{red}{+} (13+x) \\\Leftrightarrow & -10x+4& = &-2+13+x \\\Leftrightarrow & -10x \color{red}{+4} & = &11 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -10x-x& = &11-4 \\\Leftrightarrow & -11x& = &7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x+6)& = & -15 \color{red}{-} (-14-5x) \\\Leftrightarrow & 6x+36& = &-15+14+5x \\\Leftrightarrow & 6x \color{red}{+36} & = &-1 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+36} \color{blue}{-36} \color{blue}{-5x} & = &-1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-36} \\\Leftrightarrow & 6x-5x& = &-1-36 \\\Leftrightarrow & x& = &-37 \\ & V = \left\{ -37 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (6x+7)& = & 1 \color{red}{-} (-6-5x) \\\Leftrightarrow & 36x+42& = &1+6+5x \\\Leftrightarrow & 36x \color{red}{+42} & = &7 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{+42} \color{blue}{-42} \color{blue}{-5x} & = &7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-42} \\\Leftrightarrow & 36x-5x& = &7-42 \\\Leftrightarrow & 31x& = &-35 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-35}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-35}{31} & & \\ & V = \left\{ \frac{-35}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-6x-1)& = & 10 \color{red}{+} (-8+x) \\\Leftrightarrow & -30x-5& = &10-8+x \\\Leftrightarrow & -30x \color{red}{-5} & = &2 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & -30x-x& = &2+5 \\\Leftrightarrow & -31x& = &7 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{7}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-7}{31} & & \\ & V = \left\{ \frac{-7}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x-6)& = & 2 \color{red}{-} (13+x) \\\Leftrightarrow & -24x-24& = &2-13-x \\\Leftrightarrow & -24x \color{red}{-24} & = &-11 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -24x+x& = &-11+24 \\\Leftrightarrow & -23x& = &13 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{13}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-13}{23} & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (6x+1)& = & -3 \color{red}{-} (13+x) \\\Leftrightarrow & 24x+4& = &-3-13-x \\\Leftrightarrow & 24x \color{red}{+4} & = &-16 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 24x+x& = &-16-4 \\\Leftrightarrow & 25x& = &-20 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-20}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x+2)& = & 12 \color{red}{+} (7-3x) \\\Leftrightarrow & -10x+10& = &12+7-3x \\\Leftrightarrow & -10x \color{red}{+10} & = &19 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & -10x+3x& = &19-10 \\\Leftrightarrow & -7x& = &9 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{9}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)