Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{8})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{25}{8}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1760}{ \color{blue}{88} }x- \frac{275}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1760x \color{red}{-275} & = & \color{red}{264x} +48 \\\Leftrightarrow & 1760x \color{red}{-275} \color{blue}{+275} \color{blue}{-264x} & = & \color{red}{264x} +48 \color{blue}{-264x} \color{blue}{+275} \\\Leftrightarrow & 1760x-264x& = & 48+275 \\\Leftrightarrow & \color{red}{1496} x& = & 323 \\\Leftrightarrow & x = \frac{323}{1496} & & \\\Leftrightarrow & x = \frac{19}{88} & & \\ & V = \left\{ \frac{19}{88} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{5})& = & 5x+\frac{5}{8} \\\Leftrightarrow & 14x+\frac{28}{5}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{560}{ \color{blue}{40} }x+ \frac{224}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 560x \color{red}{+224} & = & \color{red}{200x} +25 \\\Leftrightarrow & 560x \color{red}{+224} \color{blue}{-224} \color{blue}{-200x} & = & \color{red}{200x} +25 \color{blue}{-200x} \color{blue}{-224} \\\Leftrightarrow & 560x-200x& = & 25-224 \\\Leftrightarrow & \color{red}{360} x& = & -199 \\\Leftrightarrow & x = \frac{-199}{360} & & \\ & V = \left\{ \frac{-199}{360} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{1}{2})& = & -3x+\frac{5}{11} \\\Leftrightarrow & -20x+\frac{5}{2}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-440}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{10}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -440x \color{red}{+55} & = & \color{red}{-66x} +10 \\\Leftrightarrow & -440x \color{red}{+55} \color{blue}{-55} \color{blue}{+66x} & = & \color{red}{-66x} +10 \color{blue}{+66x} \color{blue}{-55} \\\Leftrightarrow & -440x+66x& = & 10-55 \\\Leftrightarrow & \color{red}{-374} x& = & -45 \\\Leftrightarrow & x = \frac{-45}{-374} & & \\\Leftrightarrow & x = \frac{45}{374} & & \\ & V = \left\{ \frac{45}{374} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{3})& = & -9x+\frac{10}{11} \\\Leftrightarrow & 20x+\frac{20}{3}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+220} & = & \color{red}{-297x} +30 \\\Leftrightarrow & 660x \color{red}{+220} \color{blue}{-220} \color{blue}{+297x} & = & \color{red}{-297x} +30 \color{blue}{+297x} \color{blue}{-220} \\\Leftrightarrow & 660x+297x& = & 30-220 \\\Leftrightarrow & \color{red}{957} x& = & -190 \\\Leftrightarrow & x = \frac{-190}{957} & & \\ & V = \left\{ \frac{-190}{957} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{8})& = & 2x+\frac{5}{11} \\\Leftrightarrow & 15x+\frac{25}{8}& = & 2x+\frac{5}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1320}{ \color{blue}{88} }x+ \frac{275}{ \color{blue}{88} })& = & (\frac{176}{ \color{blue}{88} }x+ \frac{40}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1320x \color{red}{+275} & = & \color{red}{176x} +40 \\\Leftrightarrow & 1320x \color{red}{+275} \color{blue}{-275} \color{blue}{-176x} & = & \color{red}{176x} +40 \color{blue}{-176x} \color{blue}{-275} \\\Leftrightarrow & 1320x-176x& = & 40-275 \\\Leftrightarrow & \color{red}{1144} x& = & -235 \\\Leftrightarrow & x = \frac{-235}{1144} & & \\ & V = \left\{ \frac{-235}{1144} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{2}{11})& = & -9x+\frac{4}{7} \\\Leftrightarrow & -8x+\frac{4}{11}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+28} & = & \color{red}{-693x} +44 \\\Leftrightarrow & -616x \color{red}{+28} \color{blue}{-28} \color{blue}{+693x} & = & \color{red}{-693x} +44 \color{blue}{+693x} \color{blue}{-28} \\\Leftrightarrow & -616x+693x& = & 44-28 \\\Leftrightarrow & \color{red}{77} x& = & 16 \\\Leftrightarrow & x = \frac{16}{77} & & \\ & V = \left\{ \frac{16}{77} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{5}{7})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{20}{7}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{+100} & = & \color{red}{245x} +42 \\\Leftrightarrow & -700x \color{red}{+100} \color{blue}{-100} \color{blue}{-245x} & = & \color{red}{245x} +42 \color{blue}{-245x} \color{blue}{-100} \\\Leftrightarrow & -700x-245x& = & 42-100 \\\Leftrightarrow & \color{red}{-945} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-945} & & \\\Leftrightarrow & x = \frac{58}{945} & & \\ & V = \left\{ \frac{58}{945} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{6})& = & -9x+\frac{8}{3} \\\Leftrightarrow & 28x+\frac{35}{6}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{168}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 168x \color{red}{+35} & = & \color{red}{-54x} +16 \\\Leftrightarrow & 168x \color{red}{+35} \color{blue}{-35} \color{blue}{+54x} & = & \color{red}{-54x} +16 \color{blue}{+54x} \color{blue}{-35} \\\Leftrightarrow & 168x+54x& = & 16-35 \\\Leftrightarrow & \color{red}{222} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{222} & & \\ & V = \left\{ \frac{-19}{222} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{11})& = & 8x+\frac{8}{7} \\\Leftrightarrow & -21x-\frac{14}{11}& = & 8x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1617}{ \color{blue}{77} }x- \frac{98}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1617x \color{red}{-98} & = & \color{red}{616x} +88 \\\Leftrightarrow & -1617x \color{red}{-98} \color{blue}{+98} \color{blue}{-616x} & = & \color{red}{616x} +88 \color{blue}{-616x} \color{blue}{+98} \\\Leftrightarrow & -1617x-616x& = & 88+98 \\\Leftrightarrow & \color{red}{-2233} x& = & 186 \\\Leftrightarrow & x = \frac{186}{-2233} & & \\\Leftrightarrow & x = \frac{-186}{2233} & & \\ & V = \left\{ \frac{-186}{2233} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{7})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -16x+\frac{16}{7}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-112}{ \color{blue}{7} }x+ \frac{16}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{+16} & = & \color{red}{49x} +3 \\\Leftrightarrow & -112x \color{red}{+16} \color{blue}{-16} \color{blue}{-49x} & = & \color{red}{49x} +3 \color{blue}{-49x} \color{blue}{-16} \\\Leftrightarrow & -112x-49x& = & 3-16 \\\Leftrightarrow & \color{red}{-161} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-161} & & \\\Leftrightarrow & x = \frac{13}{161} & & \\ & V = \left\{ \frac{13}{161} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{9})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -10x-\frac{8}{9}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-8} & = & \color{red}{63x} +6 \\\Leftrightarrow & -90x \color{red}{-8} \color{blue}{+8} \color{blue}{-63x} & = & \color{red}{63x} +6 \color{blue}{-63x} \color{blue}{+8} \\\Leftrightarrow & -90x-63x& = & 6+8 \\\Leftrightarrow & \color{red}{-153} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-153} & & \\\Leftrightarrow & x = \frac{-14}{153} & & \\ & V = \left\{ \frac{-14}{153} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{7})& = & 8x+\frac{10}{9} \\\Leftrightarrow & -15x-\frac{15}{7}& = & 8x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x- \frac{135}{ \color{blue}{63} })& = & (\frac{504}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{-135} & = & \color{red}{504x} +70 \\\Leftrightarrow & -945x \color{red}{-135} \color{blue}{+135} \color{blue}{-504x} & = & \color{red}{504x} +70 \color{blue}{-504x} \color{blue}{+135} \\\Leftrightarrow & -945x-504x& = & 70+135 \\\Leftrightarrow & \color{red}{-1449} x& = & 205 \\\Leftrightarrow & x = \frac{205}{-1449} & & \\\Leftrightarrow & x = \frac{-205}{1449} & & \\ & V = \left\{ \frac{-205}{1449} \right\} & \\\end{align}\)