Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (3x+6)& = & -9 \color{red}{+} (2-5x) \\\Leftrightarrow & 18x+36& = &-9+2-5x \\\Leftrightarrow & 18x \color{red}{+36} & = &-7 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &-7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & 18x+5x& = &-7-36 \\\Leftrightarrow & 23x& = &-43 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-43}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-43}{23} & & \\ & V = \left\{ \frac{-43}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x-1)& = & -14 \color{red}{+} (12+x) \\\Leftrightarrow & -15x-5& = &-14+12+x \\\Leftrightarrow & -15x \color{red}{-5} & = &-2 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & -15x-x& = &-2+5 \\\Leftrightarrow & -16x& = &3 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{3}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-3}{16} & & \\ & V = \left\{ \frac{-3}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-2x+5)& = & 12 \color{red}{+} (5+x) \\\Leftrightarrow & -6x+15& = &12+5+x \\\Leftrightarrow & -6x \color{red}{+15} & = &17 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -6x-x& = &17-15 \\\Leftrightarrow & -7x& = &2 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{2}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (4x-2)& = & -9 \color{red}{+} (-14-5x) \\\Leftrightarrow & 8x-4& = &-9-14-5x \\\Leftrightarrow & 8x \color{red}{-4} & = &-23 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+5x} & = &-23 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+4} \\\Leftrightarrow & 8x+5x& = &-23+4 \\\Leftrightarrow & 13x& = &-19 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-19}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-19}{13} & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (6x-2)& = & -8 \color{red}{-} (14+x) \\\Leftrightarrow & 30x-10& = &-8-14-x \\\Leftrightarrow & 30x \color{red}{-10} & = &-22 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 30x+x& = &-22+10 \\\Leftrightarrow & 31x& = &-12 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-12}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-12}{31} & & \\ & V = \left\{ \frac{-12}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-3x+7)& = & -7 \color{red}{-} (-6+x) \\\Leftrightarrow & -12x+28& = &-7+6-x \\\Leftrightarrow & -12x \color{red}{+28} & = &-1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -12x+x& = &-1-28 \\\Leftrightarrow & -11x& = &-29 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-29}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{29}{11} & & \\ & V = \left\{ \frac{29}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x+6)& = & 15 \color{red}{+} (-5+x) \\\Leftrightarrow & -30x+30& = &15-5+x \\\Leftrightarrow & -30x \color{red}{+30} & = &10 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -30x-x& = &10-30 \\\Leftrightarrow & -31x& = &-20 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-20}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{20}{31} & & \\ & V = \left\{ \frac{20}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (3x-4)& = & -9 \color{red}{-} (10+x) \\\Leftrightarrow & 6x-8& = &-9-10-x \\\Leftrightarrow & 6x \color{red}{-8} & = &-19 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 6x+x& = &-19+8 \\\Leftrightarrow & 7x& = &-11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-5x-4)& = & 5 \color{red}{+} (7-3x) \\\Leftrightarrow & -10x-8& = &5+7-3x \\\Leftrightarrow & -10x \color{red}{-8} & = &12 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -10x+3x& = &12+8 \\\Leftrightarrow & -7x& = &20 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{20}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-20}{7} & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (6x-7)& = & -9 \color{red}{+} (-9+x) \\\Leftrightarrow & 24x-28& = &-9-9+x \\\Leftrightarrow & 24x \color{red}{-28} & = &-18 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 24x-x& = &-18+28 \\\Leftrightarrow & 23x& = &10 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{10}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{10}{23} & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x+7)& = & 3 \color{red}{-} (12-5x) \\\Leftrightarrow & 6x+14& = &3-12+5x \\\Leftrightarrow & 6x \color{red}{+14} & = &-9 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+14} \color{blue}{-14} \color{blue}{-5x} & = &-9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-14} \\\Leftrightarrow & 6x-5x& = &-9-14 \\\Leftrightarrow & x& = &-23 \\ & V = \left\{ -23 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (6x+5)& = & 13 \color{red}{+} (-3+x) \\\Leftrightarrow & 18x+15& = &13-3+x \\\Leftrightarrow & 18x \color{red}{+15} & = &10 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 18x-x& = &10-15 \\\Leftrightarrow & 17x& = &-5 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-5}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-5}{17} & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)