Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & -3x+\frac{7}{9} \\\Leftrightarrow & 20x+\frac{12}{5}& = & -3x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{+108} & = & \color{red}{-135x} +35 \\\Leftrightarrow & 900x \color{red}{+108} \color{blue}{-108} \color{blue}{+135x} & = & \color{red}{-135x} +35 \color{blue}{+135x} \color{blue}{-108} \\\Leftrightarrow & 900x+135x& = & 35-108 \\\Leftrightarrow & \color{red}{1035} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{1035} & & \\ & V = \left\{ \frac{-73}{1035} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & 8x+\frac{2}{3} \\\Leftrightarrow & 15x+\frac{12}{5}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{+36} & = & \color{red}{120x} +10 \\\Leftrightarrow & 225x \color{red}{+36} \color{blue}{-36} \color{blue}{-120x} & = & \color{red}{120x} +10 \color{blue}{-120x} \color{blue}{-36} \\\Leftrightarrow & 225x-120x& = & 10-36 \\\Leftrightarrow & \color{red}{105} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{105} & & \\ & V = \left\{ \frac{-26}{105} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{11})& = & 8x+\frac{4}{3} \\\Leftrightarrow & -21x-\frac{28}{11}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x- \frac{84}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{-84} & = & \color{red}{264x} +44 \\\Leftrightarrow & -693x \color{red}{-84} \color{blue}{+84} \color{blue}{-264x} & = & \color{red}{264x} +44 \color{blue}{-264x} \color{blue}{+84} \\\Leftrightarrow & -693x-264x& = & 44+84 \\\Leftrightarrow & \color{red}{-957} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-957} & & \\\Leftrightarrow & x = \frac{-128}{957} & & \\ & V = \left\{ \frac{-128}{957} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -16x+\frac{16}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x+ \frac{48}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{+48} & = & \color{red}{-105x} +50 \\\Leftrightarrow & -240x \color{red}{+48} \color{blue}{-48} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{-48} \\\Leftrightarrow & -240x+105x& = & 50-48 \\\Leftrightarrow & \color{red}{-135} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-135} & & \\\Leftrightarrow & x = \frac{-2}{135} & & \\ & V = \left\{ \frac{-2}{135} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{6})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -25x-\frac{25}{6}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-150}{ \color{blue}{6} }x- \frac{25}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -150x \color{red}{-25} & = & \color{red}{-54x} +4 \\\Leftrightarrow & -150x \color{red}{-25} \color{blue}{+25} \color{blue}{+54x} & = & \color{red}{-54x} +4 \color{blue}{+54x} \color{blue}{+25} \\\Leftrightarrow & -150x+54x& = & 4+25 \\\Leftrightarrow & \color{red}{-96} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-96} & & \\\Leftrightarrow & x = \frac{-29}{96} & & \\ & V = \left\{ \frac{-29}{96} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{7})& = & 7x+\frac{5}{8} \\\Leftrightarrow & -20x-\frac{10}{7}& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1120}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1120x \color{red}{-80} & = & \color{red}{392x} +35 \\\Leftrightarrow & -1120x \color{red}{-80} \color{blue}{+80} \color{blue}{-392x} & = & \color{red}{392x} +35 \color{blue}{-392x} \color{blue}{+80} \\\Leftrightarrow & -1120x-392x& = & 35+80 \\\Leftrightarrow & \color{red}{-1512} x& = & 115 \\\Leftrightarrow & x = \frac{115}{-1512} & & \\\Leftrightarrow & x = \frac{-115}{1512} & & \\ & V = \left\{ \frac{-115}{1512} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{7})& = & -4x+\frac{8}{3} \\\Leftrightarrow & -18x+\frac{30}{7}& = & -4x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-378}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-84}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -378x \color{red}{+90} & = & \color{red}{-84x} +56 \\\Leftrightarrow & -378x \color{red}{+90} \color{blue}{-90} \color{blue}{+84x} & = & \color{red}{-84x} +56 \color{blue}{+84x} \color{blue}{-90} \\\Leftrightarrow & -378x+84x& = & 56-90 \\\Leftrightarrow & \color{red}{-294} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-294} & & \\\Leftrightarrow & x = \frac{17}{147} & & \\ & V = \left\{ \frac{17}{147} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & -3x+\frac{3}{8} \\\Leftrightarrow & -20x-\frac{16}{7}& = & -3x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1120}{ \color{blue}{56} }x- \frac{128}{ \color{blue}{56} })& = & (\frac{-168}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1120x \color{red}{-128} & = & \color{red}{-168x} +21 \\\Leftrightarrow & -1120x \color{red}{-128} \color{blue}{+128} \color{blue}{+168x} & = & \color{red}{-168x} +21 \color{blue}{+168x} \color{blue}{+128} \\\Leftrightarrow & -1120x+168x& = & 21+128 \\\Leftrightarrow & \color{red}{-952} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-952} & & \\\Leftrightarrow & x = \frac{-149}{952} & & \\ & V = \left\{ \frac{-149}{952} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{3})& = & -3x+\frac{7}{3} \\\Leftrightarrow & 20x+\frac{16}{3}& = & -3x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x+ \frac{16}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{+16} & = & \color{red}{-9x} +7 \\\Leftrightarrow & 60x \color{red}{+16} \color{blue}{-16} \color{blue}{+9x} & = & \color{red}{-9x} +7 \color{blue}{+9x} \color{blue}{-16} \\\Leftrightarrow & 60x+9x& = & 7-16 \\\Leftrightarrow & \color{red}{69} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{69} & & \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & -2x+\frac{4}{7} \\\Leftrightarrow & 21x-\frac{21}{8}& = & -2x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1176}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{-112}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1176x \color{red}{-147} & = & \color{red}{-112x} +32 \\\Leftrightarrow & 1176x \color{red}{-147} \color{blue}{+147} \color{blue}{+112x} & = & \color{red}{-112x} +32 \color{blue}{+112x} \color{blue}{+147} \\\Leftrightarrow & 1176x+112x& = & 32+147 \\\Leftrightarrow & \color{red}{1288} x& = & 179 \\\Leftrightarrow & x = \frac{179}{1288} & & \\ & V = \left\{ \frac{179}{1288} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{7})& = & 5x+\frac{7}{11} \\\Leftrightarrow & 12x-\frac{18}{7}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{198}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-198} & = & \color{red}{385x} +49 \\\Leftrightarrow & 924x \color{red}{-198} \color{blue}{+198} \color{blue}{-385x} & = & \color{red}{385x} +49 \color{blue}{-385x} \color{blue}{+198} \\\Leftrightarrow & 924x-385x& = & 49+198 \\\Leftrightarrow & \color{red}{539} x& = & 247 \\\Leftrightarrow & x = \frac{247}{539} & & \\ & V = \left\{ \frac{247}{539} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & 9x+\frac{8}{5} \\\Leftrightarrow & 8x+\frac{12}{5}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{40}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{45}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 40x \color{red}{+12} & = & \color{red}{45x} +8 \\\Leftrightarrow & 40x \color{red}{+12} \color{blue}{-12} \color{blue}{-45x} & = & \color{red}{45x} +8 \color{blue}{-45x} \color{blue}{-12} \\\Leftrightarrow & 40x-45x& = & 8-12 \\\Leftrightarrow & \color{red}{-5} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-5} & & \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)