Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

1. \(-2(2x+\frac{5}{11})=5x+\frac{3}{4}\)
2. \(5(4x+\frac{4}{9})=9x+\frac{10}{11}\)
3. \(-7(4x+2)=3x+\frac{3}{4}\)
4. \(-4(5x+\frac{2}{11})=7x+\frac{2}{3}\)
5. \(5(2x+\frac{2}{7})=7x+\frac{9}{11}\)
6. \(-4(-5x-\frac{2}{3})=-9x+\frac{9}{2}\)
7. \(-4(-4x-\frac{4}{11})=3x+\frac{3}{10}\)
8. \(-5(5x-\frac{5}{11})=-6x+\frac{4}{7}\)
9. \(-3(-2x-\frac{2}{7})=-7x+\frac{3}{2}\)
10. \(3(-2x+\frac{2}{11})=-7x+\frac{2}{3}\)
11. \(-3(3x-\frac{5}{4})=7x+\frac{9}{4}\)
12. \(-7(-3x-\frac{4}{11})=4x+\frac{9}{4}\)

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{11})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -4x-\frac{10}{11}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-176}{ \color{blue}{44} }x- \frac{40}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -176x \color{red}{-40} & = & \color{red}{220x} +33 \\\Leftrightarrow & -176x \color{red}{-40} \color{blue}{+40} \color{blue}{-220x} & = & \color{red}{220x} +33 \color{blue}{-220x} \color{blue}{+40} \\\Leftrightarrow & -176x-220x& = & 33+40 \\\Leftrightarrow & \color{red}{-396} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-396} & & \\\Leftrightarrow & x = \frac{-73}{396} & & \\ & V = \left\{ \frac{-73}{396} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{4}{9})& = & 9x+\frac{10}{11} \\\Leftrightarrow & 20x+\frac{20}{9}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x+ \frac{220}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{+220} & = & \color{red}{891x} +90 \\\Leftrightarrow & 1980x \color{red}{+220} \color{blue}{-220} \color{blue}{-891x} & = & \color{red}{891x} +90 \color{blue}{-891x} \color{blue}{-220} \\\Leftrightarrow & 1980x-891x& = & 90-220 \\\Leftrightarrow & \color{red}{1089} x& = & -130 \\\Leftrightarrow & x = \frac{-130}{1089} & & \\ & V = \left\{ \frac{-130}{1089} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+2)& = & 3x+\frac{3}{4} \\\Leftrightarrow & -28x-14& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 1 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-112}{ \color{blue}{4} }x- \frac{56}{ \color{blue}{4} })& = & (\frac{12}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -112x \color{red}{-56} & = & \color{red}{12x} +3 \\\Leftrightarrow & -112x \color{red}{-56} \color{blue}{+56} \color{blue}{-12x} & = & \color{red}{12x} +3 \color{blue}{-12x} \color{blue}{+56} \\\Leftrightarrow & -112x-12x& = & 3+56 \\\Leftrightarrow & \color{red}{-124} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-124} & & \\\Leftrightarrow & x = \frac{-59}{124} & & \\ & V = \left\{ \frac{-59}{124} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -20x-\frac{8}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-24} & = & \color{red}{231x} +22 \\\Leftrightarrow & -660x \color{red}{-24} \color{blue}{+24} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{+24} \\\Leftrightarrow & -660x-231x& = & 22+24 \\\Leftrightarrow & \color{red}{-891} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-891} & & \\\Leftrightarrow & x = \frac{-46}{891} & & \\ & V = \left\{ \frac{-46}{891} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{2}{7})& = & 7x+\frac{9}{11} \\\Leftrightarrow & 10x+\frac{10}{7}& = & 7x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+110} & = & \color{red}{539x} +63 \\\Leftrightarrow & 770x \color{red}{+110} \color{blue}{-110} \color{blue}{-539x} & = & \color{red}{539x} +63 \color{blue}{-539x} \color{blue}{-110} \\\Leftrightarrow & 770x-539x& = & 63-110 \\\Leftrightarrow & \color{red}{231} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{231} & & \\ & V = \left\{ \frac{-47}{231} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{3})& = & -9x+\frac{9}{2} \\\Leftrightarrow & 20x+\frac{8}{3}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{+16} & = & \color{red}{-54x} +27 \\\Leftrightarrow & 120x \color{red}{+16} \color{blue}{-16} \color{blue}{+54x} & = & \color{red}{-54x} +27 \color{blue}{+54x} \color{blue}{-16} \\\Leftrightarrow & 120x+54x& = & 27-16 \\\Leftrightarrow & \color{red}{174} x& = & 11 \\\Leftrightarrow & x = \frac{11}{174} & & \\ & V = \left\{ \frac{11}{174} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{11})& = & 3x+\frac{3}{10} \\\Leftrightarrow & 16x+\frac{16}{11}& = & 3x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1760}{ \color{blue}{110} }x+ \frac{160}{ \color{blue}{110} })& = & (\frac{330}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1760x \color{red}{+160} & = & \color{red}{330x} +33 \\\Leftrightarrow & 1760x \color{red}{+160} \color{blue}{-160} \color{blue}{-330x} & = & \color{red}{330x} +33 \color{blue}{-330x} \color{blue}{-160} \\\Leftrightarrow & 1760x-330x& = & 33-160 \\\Leftrightarrow & \color{red}{1430} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{1430} & & \\ & V = \left\{ \frac{-127}{1430} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{11})& = & -6x+\frac{4}{7} \\\Leftrightarrow & -25x+\frac{25}{11}& = & -6x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1925}{ \color{blue}{77} }x+ \frac{175}{ \color{blue}{77} })& = & (\frac{-462}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1925x \color{red}{+175} & = & \color{red}{-462x} +44 \\\Leftrightarrow & -1925x \color{red}{+175} \color{blue}{-175} \color{blue}{+462x} & = & \color{red}{-462x} +44 \color{blue}{+462x} \color{blue}{-175} \\\Leftrightarrow & -1925x+462x& = & 44-175 \\\Leftrightarrow & \color{red}{-1463} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{-1463} & & \\\Leftrightarrow & x = \frac{131}{1463} & & \\ & V = \left\{ \frac{131}{1463} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{2}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 6x+\frac{6}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{+12} & = & \color{red}{-98x} +21 \\\Leftrightarrow & 84x \color{red}{+12} \color{blue}{-12} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{-12} \\\Leftrightarrow & 84x+98x& = & 21-12 \\\Leftrightarrow & \color{red}{182} x& = & 9 \\\Leftrightarrow & x = \frac{9}{182} & & \\ & V = \left\{ \frac{9}{182} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{11})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{6}{11}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{+18} & = & \color{red}{-231x} +22 \\\Leftrightarrow & -198x \color{red}{+18} \color{blue}{-18} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{-18} \\\Leftrightarrow & -198x+231x& = & 22-18 \\\Leftrightarrow & \color{red}{33} x& = & 4 \\\Leftrightarrow & x = \frac{4}{33} & & \\ & V = \left\{ \frac{4}{33} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{4})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -9x+\frac{15}{4}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-36}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -36x \color{red}{+15} & = & \color{red}{28x} +9 \\\Leftrightarrow & -36x \color{red}{+15} \color{blue}{-15} \color{blue}{-28x} & = & \color{red}{28x} +9 \color{blue}{-28x} \color{blue}{-15} \\\Leftrightarrow & -36x-28x& = & 9-15 \\\Leftrightarrow & \color{red}{-64} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-64} & & \\\Leftrightarrow & x = \frac{3}{32} & & \\ & V = \left\{ \frac{3}{32} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{4}{11})& = & 4x+\frac{9}{4} \\\Leftrightarrow & 21x+\frac{28}{11}& = & 4x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{924}{ \color{blue}{44} }x+ \frac{112}{ \color{blue}{44} })& = & (\frac{176}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 924x \color{red}{+112} & = & \color{red}{176x} +99 \\\Leftrightarrow & 924x \color{red}{+112} \color{blue}{-112} \color{blue}{-176x} & = & \color{red}{176x} +99 \color{blue}{-176x} \color{blue}{-112} \\\Leftrightarrow & 924x-176x& = & 99-112 \\\Leftrightarrow & \color{red}{748} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{748} & & \\ & V = \left\{ \frac{-13}{748} \right\} & \\\end{align}\)