Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{7})& = & -5x+\frac{5}{8} \\\Leftrightarrow & 6x+\frac{6}{7}& = & -5x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{336}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 336x \color{red}{+48} & = & \color{red}{-280x} +35 \\\Leftrightarrow & 336x \color{red}{+48} \color{blue}{-48} \color{blue}{+280x} & = & \color{red}{-280x} +35 \color{blue}{+280x} \color{blue}{-48} \\\Leftrightarrow & 336x+280x& = & 35-48 \\\Leftrightarrow & \color{red}{616} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{616} & & \\ & V = \left\{ \frac{-13}{616} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{4})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -12x-\frac{15}{4}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-48}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{20}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -48x \color{red}{-15} & = & \color{red}{20x} +3 \\\Leftrightarrow & -48x \color{red}{-15} \color{blue}{+15} \color{blue}{-20x} & = & \color{red}{20x} +3 \color{blue}{-20x} \color{blue}{+15} \\\Leftrightarrow & -48x-20x& = & 3+15 \\\Leftrightarrow & \color{red}{-68} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-68} & & \\\Leftrightarrow & x = \frac{-9}{34} & & \\ & V = \left\{ \frac{-9}{34} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -24x+\frac{24}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{25x} +6 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{-24} \\\Leftrightarrow & -120x-25x& = & 6-24 \\\Leftrightarrow & \color{red}{-145} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-145} & & \\\Leftrightarrow & x = \frac{18}{145} & & \\ & V = \left\{ \frac{18}{145} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{3}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 30x+\frac{18}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{+126} & = & \color{red}{-539x} +110 \\\Leftrightarrow & 2310x \color{red}{+126} \color{blue}{-126} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{-126} \\\Leftrightarrow & 2310x+539x& = & 110-126 \\\Leftrightarrow & \color{red}{2849} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{2849} & & \\ & V = \left\{ \frac{-16}{2849} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{11})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{+18} & = & \color{red}{77x} +6 \\\Leftrightarrow & -330x \color{red}{+18} \color{blue}{-18} \color{blue}{-77x} & = & \color{red}{77x} +6 \color{blue}{-77x} \color{blue}{-18} \\\Leftrightarrow & -330x-77x& = & 6-18 \\\Leftrightarrow & \color{red}{-407} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-407} & & \\\Leftrightarrow & x = \frac{12}{407} & & \\ & V = \left\{ \frac{12}{407} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+66} & = & \color{red}{-539x} +70 \\\Leftrightarrow & -462x \color{red}{+66} \color{blue}{-66} \color{blue}{+539x} & = & \color{red}{-539x} +70 \color{blue}{+539x} \color{blue}{-66} \\\Leftrightarrow & -462x+539x& = & 70-66 \\\Leftrightarrow & \color{red}{77} x& = & 4 \\\Leftrightarrow & x = \frac{4}{77} & & \\ & V = \left\{ \frac{4}{77} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{5}{8})& = & -8x+\frac{5}{8} \\\Leftrightarrow & -15x+\frac{25}{8}& = & -8x+\frac{5}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-120}{ \color{blue}{8} }x+ \frac{25}{ \color{blue}{8} })& = & (\frac{-64}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -120x \color{red}{+25} & = & \color{red}{-64x} +5 \\\Leftrightarrow & -120x \color{red}{+25} \color{blue}{-25} \color{blue}{+64x} & = & \color{red}{-64x} +5 \color{blue}{+64x} \color{blue}{-25} \\\Leftrightarrow & -120x+64x& = & 5-25 \\\Leftrightarrow & \color{red}{-56} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-56} & & \\\Leftrightarrow & x = \frac{5}{14} & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{5}{2})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 14x+\frac{35}{2}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x+ \frac{105}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{+105} & = & \color{red}{18x} +4 \\\Leftrightarrow & 84x \color{red}{+105} \color{blue}{-105} \color{blue}{-18x} & = & \color{red}{18x} +4 \color{blue}{-18x} \color{blue}{-105} \\\Leftrightarrow & 84x-18x& = & 4-105 \\\Leftrightarrow & \color{red}{66} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{66} & & \\ & V = \left\{ \frac{-101}{66} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & -9x+\frac{9}{7} \\\Leftrightarrow & 14x+\frac{21}{8}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{784}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{72}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 784x \color{red}{+147} & = & \color{red}{-504x} +72 \\\Leftrightarrow & 784x \color{red}{+147} \color{blue}{-147} \color{blue}{+504x} & = & \color{red}{-504x} +72 \color{blue}{+504x} \color{blue}{-147} \\\Leftrightarrow & 784x+504x& = & 72-147 \\\Leftrightarrow & \color{red}{1288} x& = & -75 \\\Leftrightarrow & x = \frac{-75}{1288} & & \\ & V = \left\{ \frac{-75}{1288} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{4}{3})& = & 9x+\frac{9}{8} \\\Leftrightarrow & -8x-\frac{16}{3}& = & 9x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-192}{ \color{blue}{24} }x- \frac{128}{ \color{blue}{24} })& = & (\frac{216}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -192x \color{red}{-128} & = & \color{red}{216x} +27 \\\Leftrightarrow & -192x \color{red}{-128} \color{blue}{+128} \color{blue}{-216x} & = & \color{red}{216x} +27 \color{blue}{-216x} \color{blue}{+128} \\\Leftrightarrow & -192x-216x& = & 27+128 \\\Leftrightarrow & \color{red}{-408} x& = & 155 \\\Leftrightarrow & x = \frac{155}{-408} & & \\\Leftrightarrow & x = \frac{-155}{408} & & \\ & V = \left\{ \frac{-155}{408} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{7})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -16x+\frac{8}{7}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-112}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{+8} & = & \color{red}{-49x} +9 \\\Leftrightarrow & -112x \color{red}{+8} \color{blue}{-8} \color{blue}{+49x} & = & \color{red}{-49x} +9 \color{blue}{+49x} \color{blue}{-8} \\\Leftrightarrow & -112x+49x& = & 9-8 \\\Leftrightarrow & \color{red}{-63} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-63} & & \\\Leftrightarrow & x = \frac{-1}{63} & & \\ & V = \left\{ \frac{-1}{63} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{5})& = & -5x+\frac{4}{7} \\\Leftrightarrow & 12x-\frac{18}{5}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{126}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-126} & = & \color{red}{-175x} +20 \\\Leftrightarrow & 420x \color{red}{-126} \color{blue}{+126} \color{blue}{+175x} & = & \color{red}{-175x} +20 \color{blue}{+175x} \color{blue}{+126} \\\Leftrightarrow & 420x+175x& = & 20+126 \\\Leftrightarrow & \color{red}{595} x& = & 146 \\\Leftrightarrow & x = \frac{146}{595} & & \\ & V = \left\{ \frac{146}{595} \right\} & \\\end{align}\)